NORTHWESTERN UNIV EVANSTON ILL TECHNOLOGICAL INST
Overview
Works:  91 works in 92 publications in 1 language and 94 library holdings 

Genres:  Academic theses 
Classifications:  TA7, 
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Most widely held works by
NORTHWESTERN UNIV EVANSTON ILL TECHNOLOGICAL INST
Interval programming: a new approach to linear programming with applications to chemical engineering problems(
Book
)
1 edition published in 1968 in English and held by 2 WorldCat member libraries worldwide
Chemical engineering problems of blending, mixing, furnace loading, etc., frequently have the form maximize c(t)x subject to b(  ) <or = A x <or = b(+) where the matrix A, vectors b(  ), b(+), c are given. We denote by interval programming, abbreviated IP, the theory, computations and applications of problems of this form. The purpose of this paper is to present a finite iterative method for solving IP called SUBOPT (abbreviation of suboptimization method) and to demonstrate its effectiveness on a cupola charging problem, a representative of interval programming problems in chemical engineering. (Author)
1 edition published in 1968 in English and held by 2 WorldCat member libraries worldwide
Chemical engineering problems of blending, mixing, furnace loading, etc., frequently have the form maximize c(t)x subject to b(  ) <or = A x <or = b(+) where the matrix A, vectors b(  ), b(+), c are given. We denote by interval programming, abbreviated IP, the theory, computations and applications of problems of this form. The purpose of this paper is to present a finite iterative method for solving IP called SUBOPT (abbreviation of suboptimization method) and to demonstrate its effectiveness on a cupola charging problem, a representative of interval programming problems in chemical engineering. (Author)
Ignition of cellulosic kindling fuels by veref radiant pulses(
Book
)
1 edition published in 1963 in English and held by 2 WorldCat member libraries worldwide
Radiant exposure values are reported for sus tained flaming ignition of black acellulose, newspaper and kraft corrugated board exposed to constantirradiance, thermal inputs of 30 ms duration and longer. The radiant exposure values are shown to be approximately proportional to the thickness of the exposed material and not strongly dependent on exposure duration for pulses this brief. The significance of sus tained flaming ignition, relative to ablation effects, for pulses of very brief duration is discussed. (Author)
1 edition published in 1963 in English and held by 2 WorldCat member libraries worldwide
Radiant exposure values are reported for sus tained flaming ignition of black acellulose, newspaper and kraft corrugated board exposed to constantirradiance, thermal inputs of 30 ms duration and longer. The radiant exposure values are shown to be approximately proportional to the thickness of the exposed material and not strongly dependent on exposure duration for pulses this brief. The significance of sus tained flaming ignition, relative to ablation effects, for pulses of very brief duration is discussed. (Author)
A rheologic investigation of the dynamic response spectra of soils : report 1 : basic concepts, equipment development and
soil testing procedures by
Robert L Kondner(
Book
)
2 editions published between 1962 and 1965 in English and held by 2 WorldCat member libraries worldwide
The basic development and operation characteristics of a high speed, explosive, pulse type compression apparatus for the dynamic testing of cohesive soils is presented. Dynamic loading is obtained by firing a Springfield 3006 cartridge charged with gunpoder into a combustion chamber. The high pressure developed drives a piston and deforms the soil specimen in unconfined compression. Details of the design, construction, and instrumentation of the device are given. In addition, performance characteristics as well as preliminary results of a limited test program are also reported. The range of the time spectrum studied is from approximately 0.1 millisecond to 5 miliseconds. The apparatus is discussed both as a tabletop device and for use in conjunction with large static type testing machines. Correlation of acceleration, velocity, displacement, and force measurements are presented and inertial effects are discussed. Test results are given for soil specimens with moisture contents ranging from 24.6 percent to 39.9 percent. Dynamic stressstrain response is represented by a hyperbolic equation and values of initial compliance are compared with the initial compliancetime spectrum developed from the results of creep and steady state vibratory test programs. Total strain and elastic strain spectra are compared and discussed in terms of applicable strains. Blast pulse response is shown to be in excellent agreement with the creepvibratory total strain response spectra. (Author)
2 editions published between 1962 and 1965 in English and held by 2 WorldCat member libraries worldwide
The basic development and operation characteristics of a high speed, explosive, pulse type compression apparatus for the dynamic testing of cohesive soils is presented. Dynamic loading is obtained by firing a Springfield 3006 cartridge charged with gunpoder into a combustion chamber. The high pressure developed drives a piston and deforms the soil specimen in unconfined compression. Details of the design, construction, and instrumentation of the device are given. In addition, performance characteristics as well as preliminary results of a limited test program are also reported. The range of the time spectrum studied is from approximately 0.1 millisecond to 5 miliseconds. The apparatus is discussed both as a tabletop device and for use in conjunction with large static type testing machines. Correlation of acceleration, velocity, displacement, and force measurements are presented and inertial effects are discussed. Test results are given for soil specimens with moisture contents ranging from 24.6 percent to 39.9 percent. Dynamic stressstrain response is represented by a hyperbolic equation and values of initial compliance are compared with the initial compliancetime spectrum developed from the results of creep and steady state vibratory test programs. Total strain and elastic strain spectra are compared and discussed in terms of applicable strains. Blast pulse response is shown to be in excellent agreement with the creepvibratory total strain response spectra. (Author)
ON A THEOREM OF FOULIS(
Book
)
1 edition published in 1963 in English and held by 1 WorldCat member library worldwide
1 edition published in 1963 in English and held by 1 WorldCat member library worldwide
On representations of semifinite programs which have no duality gaps by
A Charnes(
Book
)
1 edition published in 1964 in English and held by 1 WorldCat member library worldwide
Duality gaps which may occur in semiinfinite programs are shown to be interpretable as a phenomenon of an improper representation of the constraint set. Thus, any semiinfinite system of linear inequalities has a canonically closed equivalent (with interior points) which has no duality gap. With respect to the original system of inequalities, duality gaps may be closed by adjoining additional linear inequalities to the original system. Also, for consistent, but not necessarily canonically closed programs, a partial regularization of original data removes duality gaps that may occur. In contrast, a new 'weakly consistent' duality theorem without duality gap may have a value determined' by an inequality which is strictly redundant with respect to the constraint set defined by the total inequality system. (Autthor)
1 edition published in 1964 in English and held by 1 WorldCat member library worldwide
Duality gaps which may occur in semiinfinite programs are shown to be interpretable as a phenomenon of an improper representation of the constraint set. Thus, any semiinfinite system of linear inequalities has a canonically closed equivalent (with interior points) which has no duality gap. With respect to the original system of inequalities, duality gaps may be closed by adjoining additional linear inequalities to the original system. Also, for consistent, but not necessarily canonically closed programs, a partial regularization of original data removes duality gaps that may occur. In contrast, a new 'weakly consistent' duality theorem without duality gap may have a value determined' by an inequality which is strictly redundant with respect to the constraint set defined by the total inequality system. (Autthor)
Chanceconstrained games with partially controllable strategies by
A Charnes(
Book
)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
The paper is directed at the investigation of relationships of chanceconstrained programming to problems in game theory. The model introduced and analyzed herein is a twoperson game model with zerosum payoff matrix in which the strategies selected by the players do not in themselves determine the payoffs, but in which random perturbations with known distributions modify the strategy of each player before actual implementation of the strategies. A major hypothesis is that, while the strategy perturbations may be random vectors with known distributions, the selection of strategies (or more accurately strategy policies) is to be made before any observations of the random variables are made so that the strategies chosen are to be 'zeroorder' decision functions of the random perturbations, in the customary terminology of chanceconstrained programming. The strategy selected by each player is to be chosen to extremize that payoff which the player can be assured with at least some (a priori specified) probability. The point of departure in formulation and analysis of the model is a chanceconstrained version of the two dual linearprogramming problems which characterize an ordinary zerosum twoperson game. A key result shows that the deterministic equivalents for these problems yield an equivalent deterministic twoperson game which is not zerosum, and that a pair of optimal strategies for the original game are given by an equilibrium point for the latter. (Author)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
The paper is directed at the investigation of relationships of chanceconstrained programming to problems in game theory. The model introduced and analyzed herein is a twoperson game model with zerosum payoff matrix in which the strategies selected by the players do not in themselves determine the payoffs, but in which random perturbations with known distributions modify the strategy of each player before actual implementation of the strategies. A major hypothesis is that, while the strategy perturbations may be random vectors with known distributions, the selection of strategies (or more accurately strategy policies) is to be made before any observations of the random variables are made so that the strategies chosen are to be 'zeroorder' decision functions of the random perturbations, in the customary terminology of chanceconstrained programming. The strategy selected by each player is to be chosen to extremize that payoff which the player can be assured with at least some (a priori specified) probability. The point of departure in formulation and analysis of the model is a chanceconstrained version of the two dual linearprogramming problems which characterize an ordinary zerosum twoperson game. A key result shows that the deterministic equivalents for these problems yield an equivalent deterministic twoperson game which is not zerosum, and that a pair of optimal strategies for the original game are given by an equilibrium point for the latter. (Author)
Crystallographic angles for alpha mercury(
Book
)
1 edition published in 1963 in English and held by 1 WorldCat member library worldwide
1 edition published in 1963 in English and held by 1 WorldCat member library worldwide
On a mixedsequential estimating procedure with application to audit tests in accounting(
Book
)
1 edition published in 1963 in English and held by 1 WorldCat member library worldwide
In a situation when both existing acceptance and survey sampling techniques present practial problems, it is desirable to have a sampling technique which combines the practical advantages of each. Such a technique is here in presented. In the control evaluation circumstance, the sampling objective is stated as discovering as rapidly as possible whether particular error ates are in an acceptable range and, if not, estimating with prescribed assurance what the error rates might be. There have been several procedures in the classical literature which use a special type of design for detecting various recording mistakes before estimation. Such methods have an aspect of a preliminary test of significance coupled with an estimation procedure. The new statistical model or estimating procedure here proposed involves the conbination of sequential and fixed size procedures since they are, respectively, most efficient for determining acceptability and confidence intervals. The resulting mixed procedure, in contrast to others in the literature, begins with the sequential part (since most of the time acceptance is to be anticipated) and continues to an priori fixed total in the event of nonacceptance. Hence the procedure yields one of two final conclusions, either to accept the prescribed hypothesis with a specified risk or error, or a confidence interval estimate of the unknown error rate. (Author)
1 edition published in 1963 in English and held by 1 WorldCat member library worldwide
In a situation when both existing acceptance and survey sampling techniques present practial problems, it is desirable to have a sampling technique which combines the practical advantages of each. Such a technique is here in presented. In the control evaluation circumstance, the sampling objective is stated as discovering as rapidly as possible whether particular error ates are in an acceptable range and, if not, estimating with prescribed assurance what the error rates might be. There have been several procedures in the classical literature which use a special type of design for detecting various recording mistakes before estimation. Such methods have an aspect of a preliminary test of significance coupled with an estimation procedure. The new statistical model or estimating procedure here proposed involves the conbination of sequential and fixed size procedures since they are, respectively, most efficient for determining acceptability and confidence intervals. The resulting mixed procedure, in contrast to others in the literature, begins with the sequential part (since most of the time acceptance is to be anticipated) and continues to an priori fixed total in the event of nonacceptance. Hence the procedure yields one of two final conclusions, either to accept the prescribed hypothesis with a specified risk or error, or a confidence interval estimate of the unknown error rate. (Author)
The kinetic equation for a dilute gas with short range forces by Stewart Michael Harris(
Book
)
1 edition published in 1964 in English and held by 1 WorldCat member library worldwide
The kinetic equation for a dilute gas with shortrange forces is derived by a method which we believe to be physically more transparent than other methods. We first derive a density expansion for the correlation functions, the coefficients of which are functionals of F, the first distribution function. These functionals relax to timeindependent functionals over a time interval t (which we argue to be of the order of the duration of a collision) after a time t sub o (which is characterized by the phases) from the initial time. The functionals contain F over the interval + and therefore the resulting kinetic equation is nonMarkoffian. The nonMarkoffian behavior is removed by further expanding the correlation functions in a parameter that is the ratio of the duration of a collision to the mean free time. The results for the correlation functions are carried to first order and agree with those of other methods for configurations where the particles are interacting, and therefore lead to the same kinetic equation, but are otherwise different. (Author)
1 edition published in 1964 in English and held by 1 WorldCat member library worldwide
The kinetic equation for a dilute gas with shortrange forces is derived by a method which we believe to be physically more transparent than other methods. We first derive a density expansion for the correlation functions, the coefficients of which are functionals of F, the first distribution function. These functionals relax to timeindependent functionals over a time interval t (which we argue to be of the order of the duration of a collision) after a time t sub o (which is characterized by the phases) from the initial time. The functionals contain F over the interval + and therefore the resulting kinetic equation is nonMarkoffian. The nonMarkoffian behavior is removed by further expanding the correlation functions in a parameter that is the ratio of the duration of a collision to the mean free time. The results for the correlation functions are carried to first order and agree with those of other methods for configurations where the particles are interacting, and therefore lead to the same kinetic equation, but are otherwise different. (Author)
Chanceconstrained games and generalized networks by
A Charnes(
Book
)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
An extension to the theory of linear programming over generalized networks is presented which replaces the generalized Kirchoff node conditions by chance constraints. The extension is motivated by a class of problems in sanitary and chemical engineering in which the nonzero entries in the generalized incidence matrix may be random variables. Duality relationships are established for appropriate pairs of such chanceconstrained programming problems by showing that their deterministic equivalents consist of a deterministic generalized network problem and its dual. It is also shown how these duality relationships may be exploited in order to obtain actual solutions to chanceconstrained generalized network problems. (Author)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
An extension to the theory of linear programming over generalized networks is presented which replaces the generalized Kirchoff node conditions by chance constraints. The extension is motivated by a class of problems in sanitary and chemical engineering in which the nonzero entries in the generalized incidence matrix may be random variables. Duality relationships are established for appropriate pairs of such chanceconstrained programming problems by showing that their deterministic equivalents consist of a deterministic generalized network problem and its dual. It is also shown how these duality relationships may be exploited in order to obtain actual solutions to chanceconstrained generalized network problems. (Author)
On some stochastic tactical antisubmarine games(
Book
)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
In this paper some mathematical models are developed of tactical problems which arise in Antisubmarine Warfare. Specifically, the authors consider a game of pursuit between a hunterkiller force, player 1, and a possible submarine, player 2. The game consists of a sequence of moves and it terminates when player 2 is caught or evades player 1. When the players move they observe the actual tactical configuration of the forces (state) and each player chooses a tactical plan from a finite collection. This joint choice of tactical plans determines an immediate payoff and a transition probability distribution over the states. Hence an expected payoff function is defined. Formally this game is a Terminating Stochastic Game and Shapley demonstrated the existence of a value and optimal strategies (solution). An iterative technique is proposed to approximate the solution to within desired accuracy. Each iteration of the technique is obtained by solving a set of linear programs
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
In this paper some mathematical models are developed of tactical problems which arise in Antisubmarine Warfare. Specifically, the authors consider a game of pursuit between a hunterkiller force, player 1, and a possible submarine, player 2. The game consists of a sequence of moves and it terminates when player 2 is caught or evades player 1. When the players move they observe the actual tactical configuration of the forces (state) and each player chooses a tactical plan from a finite collection. This joint choice of tactical plans determines an immediate payoff and a transition probability distribution over the states. Hence an expected payoff function is defined. Formally this game is a Terminating Stochastic Game and Shapley demonstrated the existence of a value and optimal strategies (solution). An iterative technique is proposed to approximate the solution to within desired accuracy. Each iteration of the technique is obtained by solving a set of linear programs
A suboptimization method for interval linear programming: a new method for linear programming(
Book
)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
An interval program is (IP) max (c, x) s.t. b = or <A = or <b+ where the matrix A, vectors c, b, b+ are given. The explicit solution of (IP) in the case that A has full row rank (A. BenIsrael and A. Charnes: 'An explicit solution of a special class of linear programming problems, ' Operations Research, forthcoming) is used here in an iterative method for solving the general (IP). This method applies to general linear programs and is shown to be a dual method with multiple substitution. Some computational experience is given. (Author)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
An interval program is (IP) max (c, x) s.t. b = or <A = or <b+ where the matrix A, vectors c, b, b+ are given. The explicit solution of (IP) in the case that A has full row rank (A. BenIsrael and A. Charnes: 'An explicit solution of a special class of linear programming problems, ' Operations Research, forthcoming) is used here in an iterative method for solving the general (IP). This method applies to general linear programs and is shown to be a dual method with multiple substitution. Some computational experience is given. (Author)
STRAIN AGING IN AG BASE A1 ALLOYS(
Book
)
1 edition published in 1960 in English and held by 1 WorldCat member library worldwide
1 edition published in 1960 in English and held by 1 WorldCat member library worldwide
Planning for liquidity in savings and loan associations(
Book
)
1 edition published in 1964 in English and held by 1 WorldCat member library worldwide
The present paper shows an application of the method of chanceconstrained programming to a case of financial planning. It is felt that this new method of programming will in the future turn out to be helpful in analyzing a wide range of problems in the field of financial budgeting and the costing of funds for corporations and financial institutions. Indeed, the method of chanceconstrained programming was explicitly developed to take care of the following two fundamental aspects of planning, both of which are characteristic of the setting of the problem in financial budgeting: (a) there are usually and typically present a large number of constraints, institutional, subjective or otherwise; and (b) the problem is one of planning in the face of an uncertain future, the chance elements entering both the object function to be optimized and the constraints. (Author)
1 edition published in 1964 in English and held by 1 WorldCat member library worldwide
The present paper shows an application of the method of chanceconstrained programming to a case of financial planning. It is felt that this new method of programming will in the future turn out to be helpful in analyzing a wide range of problems in the field of financial budgeting and the costing of funds for corporations and financial institutions. Indeed, the method of chanceconstrained programming was explicitly developed to take care of the following two fundamental aspects of planning, both of which are characteristic of the setting of the problem in financial budgeting: (a) there are usually and typically present a large number of constraints, institutional, subjective or otherwise; and (b) the problem is one of planning in the face of an uncertain future, the chance elements entering both the object function to be optimized and the constraints. (Author)
Further explorations in the theory of multiple budgeted goals by
A Charnes(
Book
)
1 edition published in 1963 in English and held by 1 WorldCat member library worldwide
1 edition published in 1963 in English and held by 1 WorldCat member library worldwide
Critical path analyses via chance constrained and stochastic programming(
Book
)
1 edition published in 1962 in English and held by 1 WorldCat member library worldwide
A question which combines statistics and linear programming considerations was first raised by G. Tintner (Econometrica 28:2, 4905, April 60). It concerns the distribution of optimum functional values when a linear programming problem has probabilistic constraints. It is proposed to accord a chance constrained programming formulation to this kind of problem and to deal with it in a way that bears on project scheduling of the kind that is usually associated with critical path analysis, for instance, in PERT. The main focus of this paper is on the statistical distributions of the project completion (and subcompletion) times. The question of total time distributions that we deal with can therefore be given a managerial policy flavor by assuming that, ab initio, a management is considering a contract for a certain project. The task sequences are known but the times are not known except in probability. Before contracting for a target completion datewith resulting delay penaltiesthis management would like to know the likely distribution of total times in order to decide whether to accept an offered contract or else bargain further on the completion dates, penalty rates and progress payments and prices. (Author)
1 edition published in 1962 in English and held by 1 WorldCat member library worldwide
A question which combines statistics and linear programming considerations was first raised by G. Tintner (Econometrica 28:2, 4905, April 60). It concerns the distribution of optimum functional values when a linear programming problem has probabilistic constraints. It is proposed to accord a chance constrained programming formulation to this kind of problem and to deal with it in a way that bears on project scheduling of the kind that is usually associated with critical path analysis, for instance, in PERT. The main focus of this paper is on the statistical distributions of the project completion (and subcompletion) times. The question of total time distributions that we deal with can therefore be given a managerial policy flavor by assuming that, ab initio, a management is considering a contract for a certain project. The task sequences are known but the times are not known except in probability. Before contracting for a target completion datewith resulting delay penaltiesthis management would like to know the likely distribution of total times in order to decide whether to accept an offered contract or else bargain further on the completion dates, penalty rates and progress payments and prices. (Author)
Saturated sand as an inelastic twophase medium by
Z. P Bažant(
Book
)
1 edition published in 1976 in English and held by 1 WorldCat member library worldwide
The inelastic densification produced by shear straining saturated sands is opposed by the elasticity of the pore water and leads to a pore pressure increase, which causes a decrease in the intergranular frictional forces and consequent liquefaction of sand mass. This inelastic densification is accompanied by an inelastic strain of the fluid phase, and the magnitude of the developed pore water pressure is the product of the inelastic densification and the densification compliance, the latter being approximately equal to the drained compressibility of the sand. The tangent (incremental) elastic moduli are expressed in terms of the drained and undrained compressibilities of the twophase medium and the compressibilities of water and the solid matter forming the grains. It is demonstrated that the volume change of the grains due to intergranular stresses has a negligible effect on the material parameters, even though it roughly equals the volume change of the grains due to the pore water pressure, which has an appreciable effect. Typical values are calculated for the material parameters. (Author)
1 edition published in 1976 in English and held by 1 WorldCat member library worldwide
The inelastic densification produced by shear straining saturated sands is opposed by the elasticity of the pore water and leads to a pore pressure increase, which causes a decrease in the intergranular frictional forces and consequent liquefaction of sand mass. This inelastic densification is accompanied by an inelastic strain of the fluid phase, and the magnitude of the developed pore water pressure is the product of the inelastic densification and the densification compliance, the latter being approximately equal to the drained compressibility of the sand. The tangent (incremental) elastic moduli are expressed in terms of the drained and undrained compressibilities of the twophase medium and the compressibilities of water and the solid matter forming the grains. It is demonstrated that the volume change of the grains due to intergranular stresses has a negligible effect on the material parameters, even though it roughly equals the volume change of the grains due to the pore water pressure, which has an appreciable effect. Typical values are calculated for the material parameters. (Author)
On explicit solutions of interval linear programs(
Book
)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
The results of A. BenIsrael and A. Charnes: 'An explicit solution of a class of special linear programming problems, ' Operations Research (forthcoming) are extended here to the case of arbitrary rank. (Author)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
The results of A. BenIsrael and A. Charnes: 'An explicit solution of a class of special linear programming problems, ' Operations Research (forthcoming) are extended here to the case of arbitrary rank. (Author)
TIMEREVERSED MOTION IN KINETIC THEORY(
Book
)
1 edition published in 1964 in English and held by 1 WorldCat member library worldwide
A set of reversible equations for F, the first distribution function and g, the correlation function, are derived for the weak force case. The 'forward motion, ' i.e., development in time from uncorrelated initial conditions, and the corresponding reverse motion are examined. In the 'forward motion' the equation for F evolves into the FokkerPlanck equation while in the corresponding reverse motion F is described by an antiFokkerPlanck equation. (Author)
1 edition published in 1964 in English and held by 1 WorldCat member library worldwide
A set of reversible equations for F, the first distribution function and g, the correlation function, are derived for the weak force case. The 'forward motion, ' i.e., development in time from uncorrelated initial conditions, and the corresponding reverse motion are examined. In the 'forward motion' the equation for F evolves into the FokkerPlanck equation while in the corresponding reverse motion F is described by an antiFokkerPlanck equation. (Author)
Extreme point solutions in mathematical programming: an opposite sign algorithm(
Book
)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
Several important and efficient methods of solution of specific types of linear programming problems have the feature of sometimes providing optimal solutions which are not extremepoint (or basic) solutions, so that important and useful analyses provided by knowledge of the optimal dual evaluators are not available. It is also often desirable to be able to begin with a solution suggested by knowledgeable persons with experience in the field (or other considerations) and to proceed immediately to a basic solution at least as good as the suggested one. In this paper it is shown how part of the technique of proof of the opposite sign theorem can be employed in a simple algorithm to achieve this end. This method is equally valid when maximizing a nonlinear but convex objective function. A tested ALGOL code is provided for executing the algorithm in a manner compatible (as a procedure) with other programs. (Author)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
Several important and efficient methods of solution of specific types of linear programming problems have the feature of sometimes providing optimal solutions which are not extremepoint (or basic) solutions, so that important and useful analyses provided by knowledge of the optimal dual evaluators are not available. It is also often desirable to be able to begin with a solution suggested by knowledgeable persons with experience in the field (or other considerations) and to proceed immediately to a basic solution at least as good as the suggested one. In this paper it is shown how part of the technique of proof of the opposite sign theorem can be employed in a simple algorithm to achieve this end. This method is equally valid when maximizing a nonlinear but convex objective function. A tested ALGOL code is provided for executing the algorithm in a manner compatible (as a procedure) with other programs. (Author)
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