Brinkhuis, Jan
Overview
Works:  43 works in 77 publications in 3 languages and 955 library holdings 

Roles:  Author, Correspondent 
Classifications:  HB141, 330.015195 
Publication Timeline
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Most widely held works by
Jan Brinkhuis
Optimization : insights and applications by
Jan Brinkhuis(
Book
)
13 editions published between 2005 and 2008 in English and held by 237 WorldCat member libraries worldwide
This selfcontained textbook is an informal introduction to optimization through the use of numerous illustrations and applications. The focus is on analytically solving optimization problems with a finite number of continuous variables. In addition, the authors provide introductions to classical and modern numerical methods of optimization and to dynamic optimization. The book's overarching point is that most problems may be solved by the direct application of the theorems of Fermat, Lagrange, and Weierstrass. The authors show how the intuition for each of the theoretical results can be supported by simple geometric figures. They include numerous applications through the use of varied classical and practical problems. Even experts may find some of these applications truly surprising. A basic mathematical knowledge is sufficient to understand the topics covered in this book. More advanced readers, even experts, will be surprised to see how all main results can be grounded on the FermatLagrange theorem. The book can be used for courses on continuous optimization, from introductory to advanced, for any field for which optimization is relevant
13 editions published between 2005 and 2008 in English and held by 237 WorldCat member libraries worldwide
This selfcontained textbook is an informal introduction to optimization through the use of numerous illustrations and applications. The focus is on analytically solving optimization problems with a finite number of continuous variables. In addition, the authors provide introductions to classical and modern numerical methods of optimization and to dynamic optimization. The book's overarching point is that most problems may be solved by the direct application of the theorems of Fermat, Lagrange, and Weierstrass. The authors show how the intuition for each of the theoretical results can be supported by simple geometric figures. They include numerous applications through the use of varied classical and practical problems. Even experts may find some of these applications truly surprising. A basic mathematical knowledge is sufficient to understand the topics covered in this book. More advanced readers, even experts, will be surprised to see how all main results can be grounded on the FermatLagrange theorem. The book can be used for courses on continuous optimization, from introductory to advanced, for any field for which optimization is relevant
Embedding problems and Galois modules by
Jan Brinkhuis(
Book
)
8 editions published between 1981 and 1982 in English and Undetermined and held by 25 WorldCat member libraries worldwide
8 editions published between 1981 and 1982 in English and Undetermined and held by 25 WorldCat member libraries worldwide
On the duality theory of convex objects by
Jan Brinkhuis(
Book
)
5 editions published in 2001 in English and held by 7 WorldCat member libraries worldwide
We consider the classical duality operators for convex objects suchas the polar of a convex set containing the origin, the dual norm,the Fencheltransform of a convex function and the conjugate of aconvex cone. We give a new, sharper, unified treatment of the theoryof these operators, deriving generalized theorems of HahnBanach,FenchelMoreau and DubovitskyMilyutin for the conjugate of convexcones in not necessarily finite dimensional vector spaces and hencefor all the other duality operators of convex objects
5 editions published in 2001 in English and held by 7 WorldCat member libraries worldwide
We consider the classical duality operators for convex objects suchas the polar of a convex set containing the origin, the dual norm,the Fencheltransform of a convex function and the conjugate of aconvex cone. We give a new, sharper, unified treatment of the theoryof these operators, deriving generalized theorems of HahnBanach,FenchelMoreau and DubovitskyMilyutin for the conjugate of convexcones in not necessarily finite dimensional vector spaces and hencefor all the other duality operators of convex objects
On the principle of FermatLagrange for Mixed SmoothConvex Extremal Problems by
Jan Brinkhuis(
Book
)
4 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
A necessary condition  the Principle of FermatLagrange  is offered for mixed smoothconvexoptimization problems. This generalizes and unifies most of the known necessary conditions forconcrete finite and infinite dimensional optimization problems of interest. The new idea in comparisonwith the unified version of Tikhomirov and others ([IT], [ATF] and [T]) is that a geometricalconstruction of the principle is given. In the present setup constraints are not mentioned explicitly, thefeasibility set is allowed to vary in a nonstandard way and the objective function is also allowed tovary. An equivalent analytical formulation is given as well; we propose a new standard form foroptimization problems which allows greater flexibility
4 editions published in 1998 in English and held by 7 WorldCat member libraries worldwide
A necessary condition  the Principle of FermatLagrange  is offered for mixed smoothconvexoptimization problems. This generalizes and unifies most of the known necessary conditions forconcrete finite and infinite dimensional optimization problems of interest. The new idea in comparisonwith the unified version of Tikhomirov and others ([IT], [ATF] and [T]) is that a geometricalconstruction of the principle is given. In the present setup constraints are not mentioned explicitly, thefeasibility set is allowed to vary in a nonstandard way and the objective function is also allowed tovary. An equivalent analytical formulation is given as well; we propose a new standard form foroptimization problems which allows greater flexibility
Optimization : insights and applications by
Jan Brinkhuis(
)
1 edition published in 2005 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 5 WorldCat member libraries worldwide
Plücker embedding of Grassmannian manifolds and the invariant theory of binary forms by
Jan Brinkhuis(
Book
)
1 edition published in 1987 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1987 in English and held by 3 WorldCat member libraries worldwide
On shadowprices : linearization by minorization in the theory of extremal problems by
Jan Brinkhuis(
Book
)
2 editions published in 1994 in Dutch and English and held by 3 WorldCat member libraries worldwide
2 editions published in 1994 in Dutch and English and held by 3 WorldCat member libraries worldwide
Normal integral bases and complex conjugation by
Jan Brinkhuis(
Book
)
1 edition published in 1986 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1986 in English and held by 3 WorldCat member libraries worldwide
Modules Galoisiens et sommes de Jacobi by
Jan Brinkhuis(
Book
)
1 edition published in 1987 in French and held by 3 WorldCat member libraries worldwide
1 edition published in 1987 in French and held by 3 WorldCat member libraries worldwide
On a geometrical construction of the multiplier rule by
Jan Brinkhuis(
Book
)
1 edition published in 1997 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1997 in English and held by 3 WorldCat member libraries worldwide
Vertical halfspaces as solutions of dual extremal problems by
Jan Brinkhuis(
Book
)
1 edition published in 1995 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1995 in English and held by 3 WorldCat member libraries worldwide
An introduction to duality in optimization theory by
Jan Brinkhuis(
Book
)
1 edition published in 1993 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 3 WorldCat member libraries worldwide
Galois modules and operations on the idelic character maps I by
Jan Brinkhuis(
Book
)
1 edition published in 1987 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1987 in English and held by 3 WorldCat member libraries worldwide
Composition of symbolical products by
Jan Brinkhuis(
Book
)
1 edition published in 1987 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1987 in English and held by 3 WorldCat member libraries worldwide
Extremal problems and inclusion of perturbations in halfspaces by
Jan Brinkhuis(
Book
)
1 edition published in 1995 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1995 in English and held by 3 WorldCat member libraries worldwide
On the complexity of the primal selfconcordant barrier method by
Jan Brinkhuis(
Book
)
2 editions published in 2000 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2000 in English and held by 2 WorldCat member libraries worldwide
Relative Galois module structure for quartic fields by
Jan Brinkhuis(
Book
)
1 edition published in 1988 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 2 WorldCat member libraries worldwide
Normal integral bases and embedding of fields by
Jan Brinkhuis(
Book
)
2 editions published in 1985 in Dutch and English and held by 2 WorldCat member libraries worldwide
2 editions published in 1985 in Dutch and English and held by 2 WorldCat member libraries worldwide
Testing concavity and quasiconcavity is easy by
Jan Brinkhuis(
Book
)
3 editions published in 1985 in English and Dutch and held by 2 WorldCat member libraries worldwide
3 editions published in 1985 in English and Dutch and held by 2 WorldCat member libraries worldwide
On a comparison of Gauss sums with products of Lagrange resolvents by
Jan Brinkhuis(
Book
)
1 edition published in 1991 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1991 in English and held by 2 WorldCat member libraries worldwide
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Related Identities
 Tikhomirov, V. M. (Vladimir Mikhaĭlovich) 1934 Author
 Erasmus Universiteit Rotterdam Econometrisch Instituut
 Tinbergen Institute
 Cohen, Arjeh M.
 Zhang, Shuzhong
 Reve, Karel van het 19211999 Recipient
 Engelman, Jan (Johannes Aloysius Antonius) 19001972 Recipient
 Slaager, R. C.
 Protassov, V.
 Tikhomirov, V.
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