摘要:

A new class of cutting planes (for integar linear programs) recently introduced by V. Chvátal is discussed. It is shown that Gomary's fundamental cuts are special cases of these cuts. A formula for the depth of a cut with respect to the cone is found. For cuts formed from from binding inequalities only, the optimal choice is reduced to a system of non-linear integar programs. It is shown that under special circumstances Chvátal's cuts formed from all inequalities can be replaced by cuts formed from binding inequalities without decreasing the depth. The above results re applied to fundamental cuts.

ISSN:0047-6277    

DOI:10.1080/02331887508801232

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

In this note we give some possibilities for evaluating resp. bounding the rank of Gomary-cuts. Furtheron we discuss the importance of such considerations in integer programming.

ISSN:0047-6277    

DOI:10.1080/02331887508801233

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

Procedures of feasible directions are established for extremal problems of the typewith continuous differentiable functions, where theare in addition convex. The procedures converge to a stationary point without making use of any antizigzag rules. Gradients and the values of the functions of all restrictions which are fulfilled as equations up to η > 0, are taken into the direction search problems.

ISSN:0047-6277    

DOI:10.1080/02331887508801234

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

We give a general construction for the composition of two algorithms. The idea is shown for the constrained optimization problem.

ISSN:0047-6277    

DOI:10.1080/02331887508801235

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

Proceeding from Zoutendijk's conception of optimal feasible directions the formation of the proceeding directions in the reduced gradient procedure is analyzed. By the minimization of the “distortion” occuring between the gradient and the proceeding direction, a modification of the choice of the direction results, which suggests a higher effectivity of the procedures.

ISSN:0047-6277    

DOI:10.1080/02331887508801236

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

A generalization of the Tucker theorem to separable Hilbert spaces, is motivated and proced without making use of interior points. For the case of polyhedral semi orderings over a cone in Rna straightforward deduction from the classical theorem is given.

ISSN:0047-6277    

DOI:10.1080/02331887508801237

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

Duality relations for various classes of complex nonlinear programming problems have recently appeared in the literaure. These problems are special cases of a complex programming problem whose objective function includes the square root of a quadratic form, and so may not be differentiable. For this problem, necessary and sufficient conditions are obtained for the existence of an optimal solution, and appropriate duality theorems are established.

ISSN:0047-6277    

DOI:10.1080/02331887508801238

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

A class of stochastic linear programs termed stable stochastic linear programs defined in terms fo convergence of sequences of stochastic linear program is introduced. A sufficient regularity condition for such stability is given, slightly stronger than the necessary and sufficient condition that a stochastic linear program (SLP) has optimal value. This is a minimal condition in a certain sense. Applications of this regularity condition to Monte Carlo methods, numerical solution of the distribution problem and two-stage programming are given.

ISSN:0047-6277    

DOI:10.1080/02331887508801239

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

A modification of a method due to L. Bittner for deriving maximum principles for optimal control problems in Banach spaces is given, where the optimal control problems have the form (1), (2). This method is applied to optimal processes described by the Ham-Merstein integral equation (26) and the more general equation (64) and (73).

ISSN:0047-6277    

DOI:10.1080/02331887508801240

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor

摘要:

In this paper we give separation theorems for convex sets of a product space. Separation is carried out by linear operators. With these theorems we prove several assertions on conjugate operators and subdifferentials of operators (which map a vector space into an order complete vector lattice), where we use the definition of conjugate operators as done by Zowe. Simultaneously we generalize some of his results to such operators. Moreover we prove that an order complete vector lattice is a vector lattice with certain separation properties.

ISSN:0047-6277    

DOI:10.1080/02331887508801242

出版商:Akademie-Verlag    

年代:1975

数据来源: Taylor