摘要:

It is shown that under rather weak differentiability and regularity assumptions, an infinite dimensional (not necessarily convex) optimization problem admits Lagrange multipliers that are minimal in a certain sense. The essential tool in establishing this statement is a result on minimal extensions of linear functionals proved earlier by the author.

ISSN:0323-3898    

DOI:10.1080/02331938108842716

出版商:Akademic-Verlag    

年代:1981

数据来源: Taylor

摘要:

We give new characterizations of the asymptotic cone and the lineality space of a convex set; to this effect we use the notions of margin, extreme point, face and cone of admissible directions. For example we find this statement: ifA. is a closed, line-free and finite-dimensional convex set, thenwherepis the set of extreme points ofAandW(A,α) is the witness cone ofAfrom the point α.

ISSN:0323-3898    

DOI:10.1080/02331938108842717

出版商:Akademic-Verlag    

年代:1981

数据来源: Taylor

摘要:

A negative answer is given to a question of KIBE: about the extension of Caristi's fixed point theorem.

ISSN:0323-3898    

DOI:10.1080/02331938108842718

出版商:Akademic-Verlag    

年代:1981

数据来源: Taylor

摘要:

To each optimization problemB(of theRn) is associated an optimization problemT(B) (of theRm) by means of an transformationT(fromRmintoRn). The investigations have the aim to find relations between convex and non convex optimization problems. From this point of view the CREMONA-transformations play an essential role.

ISSN:0323-3898    

DOI:10.1080/02331938108842719

出版商:Akademic-Verlag    

年代:1981

数据来源: Taylor

摘要:

In the paper necessary and sufficient conditions are presented for the boundedness below of convex, concave and quadratic functions on the set of (mixed)-integer point of a convex polyhedral set with a rational description.

ISSN:0323-3898    

DOI:10.1080/02331938108842720

出版商:Akademic-Verlag    

年代:1981

数据来源: Taylor

摘要:

Every convex program can be rewritten as a stable program after identifying the minimal index set of binding constraints. This paper suggests a finite iterative method for calculating this particular set of indices. The method is demonstrated on such diverse problems as characterizing a PABETG optimum in multicriteria optimization and solving differentiable convex programs by the method of augmented Lagrangians without assuming a regularization condition. Some results extend to arbitrary convex cones and abstract spaces, and apply to optimal control problems.

ISSN:0323-3898    

DOI:10.1080/02331938108842721

出版商:Akademic-Verlag    

年代:1981

数据来源: Taylor

摘要:

There are solvable linear complementarity problems which can not be solved by the algorithm of Lemke. In such a case this algorithm injures at an edge-ray. To continue the search we permit also passages over edge-rays of the feasible region. These can be executed by the simplex-method. It is possible to keep Lemke's combinatoric pivoting rule. The extended algorithm solves all problems solvable also by Lemke' method and others.

ISSN:0323-3898    

DOI:10.1080/02331938108842722

出版商:Akademic-Verlag    

年代:1981

数据来源: Taylor

摘要:

A solution method is presented for solving of general linear complementary problems of the form. The procedure is based on the solution of an one-parametric linear optimization problem. The algorithm is demonstrated for an example. It is implemented in PL1 and tested on a computer of the type ES 1022.

ISSN:0323-3898    

DOI:10.1080/02331938108842723

出版商:Akademic-Verlag    

年代:1981

数据来源: Taylor

摘要:

The joint chance constrained extremum problem is considered. Basing on independent realizations of a random vector the Parzen kernel-type estimate of the constraint function is proposed. The initial problem and the problem where the constraint function is replaced by this estimate are compared.

ISSN:0323-3898    

DOI:10.1080/02331938108842724

出版商:Akademic-Verlag    

年代:1981

数据来源: Taylor

摘要:

In this paper, for certain subfamilies of the family of bounded measurable two-person games in normal form, the value sets are characterized by three properties, called the maximum property, the minimum property and the adjunction property. Furthermore, one of the papers of Vilkas is critically discussed. Finally, for bimatrix games, two systems of characterizing properties for the equilibrium point sets are given.

ISSN:0323-3898    

DOI:10.1080/02331938108842725

出版商:Akademic-Verlag    

年代:1981

数据来源: Taylor