Eichfelder, Gabriele
Overview
Works:  58 works in 113 publications in 2 languages and 1,117 library holdings 

Roles:  Author, Other, Contributor, dgs, htt, Editor 
Classifications:  QA402.5, 519.3 
Publication Timeline
.
Most widely held works by
Gabriele Eichfelder
Adaptive scalarization methods in multiobjective optimization by
Gabriele Eichfelder(
)
21 editions published between 2006 and 2010 in English and Undetermined and held by 556 WorldCat member libraries worldwide
"This book presents new adaptive solution methods for multiobjective optimization problems based on parameter dependent scalarizations. With the help of sensitivity results an adaptive parameter control is developed so that highquality approximations of the efficient set are generated. These examinations are based on a general scalarization approach for arbitrary partial orderings defined by a closed pointed convex cone in the objective space. The application of the results to many other wellknown scalarization methods is also presented. Background material of multiobjective optimization and scalarization approaches is concisely summarized at the beginning. The effectiveness of these new methods is demonstrated by test problems and a recent problem in intensitymodulated radiotherapy. The book concludes with a further application: a procedure for solving multiobjective bilevel optimization problems."Jacket
21 editions published between 2006 and 2010 in English and Undetermined and held by 556 WorldCat member libraries worldwide
"This book presents new adaptive solution methods for multiobjective optimization problems based on parameter dependent scalarizations. With the help of sensitivity results an adaptive parameter control is developed so that highquality approximations of the efficient set are generated. These examinations are based on a general scalarization approach for arbitrary partial orderings defined by a closed pointed convex cone in the objective space. The application of the results to many other wellknown scalarization methods is also presented. Background material of multiobjective optimization and scalarization approaches is concisely summarized at the beginning. The effectiveness of these new methods is demonstrated by test problems and a recent problem in intensitymodulated radiotherapy. The book concludes with a further application: a procedure for solving multiobjective bilevel optimization problems."Jacket
Variable ordering structures in vector optimization by
Gabriele Eichfelder(
)
16 editions published between 2014 and 2016 in English and held by 334 WorldCat member libraries worldwide
This book provides an introduction to vector optimization with variable ordering structures, i.e., to optimization problems with a vectorvalued objective function where the elements in the objective space are compared based on a variable ordering structure: instead of a partial ordering defined by a convex cone, we see a whole family of convex cones, one attached to each element of the objective space.The book starts by presenting several applications that have recently sparked new interest in these optimization problems, and goes on to discuss fundamentals and important results on a wide range of topics. The theory developed includes various optimality notions, linear and nonlinear scalarization functionals, optimality conditions of Fermat and Lagrange type, existence and duality results. The book closes with a collection of numerical approaches for solving these problems in practice
16 editions published between 2014 and 2016 in English and held by 334 WorldCat member libraries worldwide
This book provides an introduction to vector optimization with variable ordering structures, i.e., to optimization problems with a vectorvalued objective function where the elements in the objective space are compared based on a variable ordering structure: instead of a partial ordering defined by a convex cone, we see a whole family of convex cones, one attached to each element of the objective space.The book starts by presenting several applications that have recently sparked new interest in these optimization problems, and goes on to discuss fundamentals and important results on a wide range of topics. The theory developed includes various optimality notions, linear and nonlinear scalarization functionals, optimality conditions of Fermat and Lagrange type, existence and duality results. The book closes with a collection of numerical approaches for solving these problems in practice
Parametergesteuerte Lösung nichtlinearer multikriterieller Optimierungsprobleme by
Gabriele Eichfelder(
)
4 editions published in 2006 in German and held by 45 WorldCat member libraries worldwide
4 editions published in 2006 in German and held by 45 WorldCat member libraries worldwide
Optimality conditions for vector optimization problems with variable ordering structures by
Gabriele Eichfelder(
)
3 editions published in 2010 in English and German and held by 20 WorldCat member libraries worldwide
3 editions published in 2010 in English and German and held by 20 WorldCat member libraries worldwide
On Minmax Robustness for Multiobjective Optimization with Decision or Parameter Uncertainty by Corinna Krüger(
)
2 editions published in 2018 in English and held by 18 WorldCat member libraries worldwide
Multiobjective optimization problems (MOPs) are problems with two or more objective functions. Two types of uncertainty in MOPs are distinguished, namely decision uncertainty and parameter uncertainty. Decision uncertainty means that solutions cannot be implemented exactly as targeted and parameter uncertainty means that a part of the problem data is unknown. In the first publication of this cumulative thesis, a minmax robustness concept for MOPs with decision uncertainty is introduced and decision robust efficient solutions are defined as the solutions to a setvalued optimization problem
2 editions published in 2018 in English and held by 18 WorldCat member libraries worldwide
Multiobjective optimization problems (MOPs) are problems with two or more objective functions. Two types of uncertainty in MOPs are distinguished, namely decision uncertainty and parameter uncertainty. Decision uncertainty means that solutions cannot be implemented exactly as targeted and parameter uncertainty means that a part of the problem data is unknown. In the first publication of this cumulative thesis, a minmax robustness concept for MOPs with decision uncertainty is introduced and decision robust efficient solutions are defined as the solutions to a setvalued optimization problem
On reformulations of nonconvex quadratic programs over convex cones by setsemidefinite constraints(
)
1 edition published in 2010 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 2010 in English and held by 16 WorldCat member libraries worldwide
On the setsemidefinite representation of nonconvex quadratic programs over arbitrary feasible sets by
Gabriele Eichfelder(
)
1 edition published in 2011 in English and held by 11 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 11 WorldCat member libraries worldwide
On the setsemidefinite representation of nonconvex quadratic programs over arbitrary feasible sets by
Gabriele Eichfelder(
Book
)
2 editions published between 2011 and 2013 in English and held by 5 WorldCat member libraries worldwide
In the paper we prove that any nonconvex quadratic problem over some set KRn with additional linear and binary constraints can be rewritten as a linear problem over the cone, dual to the cone of Ksemidefinite matrices. We show that when K is defined by one quadratic constraint or by one concave quadratic constraint and one linear inequality, then the resulting Ksemidefinite problem is actually a semidefinite programming problem. This generalizes results obtained by Sturm and Zhang (Math Oper Res 28:246267, 2003). Our result also generalizes the wellknown completely positive representation result from Burer (Math Program 120:479495, 2009), which is actually a special instance of our result with K=Rn+
2 editions published between 2011 and 2013 in English and held by 5 WorldCat member libraries worldwide
In the paper we prove that any nonconvex quadratic problem over some set KRn with additional linear and binary constraints can be rewritten as a linear problem over the cone, dual to the cone of Ksemidefinite matrices. We show that when K is defined by one quadratic constraint or by one concave quadratic constraint and one linear inequality, then the resulting Ksemidefinite problem is actually a semidefinite programming problem. This generalizes results obtained by Sturm and Zhang (Math Oper Res 28:246267, 2003). Our result also generalizes the wellknown completely positive representation result from Burer (Math Program 120:479495, 2009), which is actually a special instance of our result with K=Rn+
On the effects of combining objectives in multiobjective optimization by
Stephan Dempe(
Book
)
2 editions published in 2014 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 2014 in English and held by 5 WorldCat member libraries worldwide
Vector optimization with a variable ordering structure by
Gabriele Eichfelder(
Book
)
2 editions published in 2009 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2009 in English and held by 4 WorldCat member libraries worldwide
Set semidefinite optimization by
Gabriele Eichfelder(
Book
)
2 editions published in 2007 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2007 in English and held by 4 WorldCat member libraries worldwide
Scalarizations for adaptively solving multiobjective optimization problems by
Gabriele Eichfelder(
Book
)
2 editions published in 2006 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2006 in English and held by 4 WorldCat member libraries worldwide
Optimality conditions for set optimization using a directional derivative based on generalized Steiner sets by
Robert Baier(
)
2 editions published in 2019 in English and held by 4 WorldCat member libraries worldwide
Setoptimization has attracted increasing interest in the last years, as for instance uncertain multiobjective optimization problems lead to such problems with a set valued objective function. Thereby, from a practical point of view, most of all the socalled set approach is of interest. However, optimality conditions for these problems, for instance using directional derivatives, are still very limited. The key aspect for a useful directional derivative is the definition of a useful set difference for the evaluation of the numerator in the difference quotient. We present here a new set difference which avoids the use of a convex hull and which applies to arbitrary convex sets, and not to strictly convex sets only. The new set difference is based on the new concept of generalized Steiner sets. We introduce the Banach space of generalized Steiner sets as well as an embedding of convex sets in this space using Steiner points. In this Banach space we can easily define a difference and a directional derivative. We use the latter for new optimality conditions for set optimization. Numerical examples illustrate the new concepts
2 editions published in 2019 in English and held by 4 WorldCat member libraries worldwide
Setoptimization has attracted increasing interest in the last years, as for instance uncertain multiobjective optimization problems lead to such problems with a set valued objective function. Thereby, from a practical point of view, most of all the socalled set approach is of interest. However, optimality conditions for these problems, for instance using directional derivatives, are still very limited. The key aspect for a useful directional derivative is the definition of a useful set difference for the evaluation of the numerator in the difference quotient. We present here a new set difference which avoids the use of a convex hull and which applies to arbitrary convex sets, and not to strictly convex sets only. The new set difference is based on the new concept of generalized Steiner sets. We introduce the Banach space of generalized Steiner sets as well as an embedding of convex sets in this space using Steiner points. In this Banach space we can easily define a difference and a directional derivative. We use the latter for new optimality conditions for set optimization. Numerical examples illustrate the new concepts
Solving nonlinear multiobjective bilevel optimization problems with coupled upper level constraints by
Gabriele Eichfelder(
Book
)
2 editions published in 2007 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2007 in English and held by 4 WorldCat member libraries worldwide
Conevalued maps in optimization by
Gabriele Eichfelder(
Book
)
1 edition published in 2011 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 4 WorldCat member libraries worldwide
On reformulations of nonconvex quadratic programs over convex cones by setsemidefinite constraints by
Gabriele Eichfelder(
Book
)
2 editions published in 2010 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2010 in English and held by 4 WorldCat member libraries worldwide
Multiobjective bilevel optimization by
Gabriele Eichfelder(
Book
)
2 editions published in 2007 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2007 in English and held by 4 WorldCat member libraries worldwide
Decision uncertainty in multiobjective optimization by
Gabriele Eichfelder(
)
2 editions published between 2016 and 2017 in English and held by 4 WorldCat member libraries worldwide
In many realworld optimization problems, a solution cannot be realized in practice exactly as computed, e.g., it may be impossible to produce a board of exactly 3.546~mm width. Whenever computed solutions are not realized exactly but in a perturbed way, we speak of decision uncertainty. We study decision uncertainty in multiobjective optimization problems and we propose the concept decision robust efficiency for evaluating the robustness of a solution in this case. Therefore, we address decision uncertainty within the framework of setvalued maps. First, we prove that convexity and continuity are preserved by the resulting setvalued mappings. Second, we obtain specific results for particular classes of objective functions that are relevant for solving the setvalued problem. We furthermore prove that decision robust efficient solutions can be found by solving a deterministic problem in case of linear objective functions. We also investigate the relationship of the proposed concept to other concepts in the literature
2 editions published between 2016 and 2017 in English and held by 4 WorldCat member libraries worldwide
In many realworld optimization problems, a solution cannot be realized in practice exactly as computed, e.g., it may be impossible to produce a board of exactly 3.546~mm width. Whenever computed solutions are not realized exactly but in a perturbed way, we speak of decision uncertainty. We study decision uncertainty in multiobjective optimization problems and we propose the concept decision robust efficiency for evaluating the robustness of a solution in this case. Therefore, we address decision uncertainty within the framework of setvalued maps. First, we prove that convexity and continuity are preserved by the resulting setvalued mappings. Second, we obtain specific results for particular classes of objective functions that are relevant for solving the setvalued problem. We furthermore prove that decision robust efficient solutions can be found by solving a deterministic problem in case of linear objective functions. We also investigate the relationship of the proposed concept to other concepts in the literature
On classes of set optimization problems which are reducible to vector optimization problems and its impact on numerical test
instances by
Gabriele Eichfelder(
)
1 edition published in 2018 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2018 in English and held by 3 WorldCat member libraries worldwide
A branchandbound based algorithm for nonconvex multiobjective optimization by
Julia Niebling(
)
1 edition published in 2018 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2018 in English and held by 3 WorldCat member libraries worldwide
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Related Identities
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 Schöbel, Anita Other
 SpringerLink (Online service) Other
 Krüger, Corinna Other Author
 Ha, Truong Xuan Duc Other
 Gerlach, Tobias Other
 Niebling, Julia Other Author
 FriedrichAlexanderUniversität ErlangenNürnberg Department Mathematik
 Thomann, Jana Other Author
 Fliege, Jörg Other
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