摘要:

Mean value theorems for nonsmooth functions are presented. Two versions are given, both using the contingent derivative. In. the first one a tangential convexity condition is used. In the second one no convexity assumption is made but the estimate.involves the contingent derivativedf (x, b − a) offat points arbitrarily close to the segment [a, b]. The proof relies on the Bishop-Phelps-Daneš-Ekeland procedure.

ISSN:0233-1934    

DOI:10.1080/02331938808843330

出版商:Akademic-Verlag    

年代:1988

数据来源: Taylor

摘要:

The common definition of directions of affinity resp. constancy of a proper convex function implicitly requires the domain of finiteness to be unbounded in these directions. This assumption is dropped here, and directions of strictness are also defined. Under a mild continuity condition it is shown that directions of affinity resp. constancy form vector spaces. Behaviour under addition and linear transformations is investigated. Particularly simple results are obtained under the assumption that any direction is either a direction of strictness or affinity. These results are used to obtain a theorem on the dimension of the minimum set of a proper convex function, as well as simple rank conditions necessary and sufficient for strict convexity of a sum, where the summands are not necessarily strictly convex. The linear Poisson model and geometric programming are treated as examples.

ISSN:0233-1934    

DOI:10.1080/02331938808843331

出版商:Akademic-Verlag    

年代:1988

数据来源: Taylor

摘要:

Müller, P.H.; V. Nollau; A.I. Polovinkin: Stochastische Suchverfahren. VEB Fachbuchverlag Leipzig 1986, 90 S., 16 Abb., 4 Tab., 16,50 M, ISBN 3-343-00163-5.

ISSN:0233-1934    

DOI:10.1080/02331938808843332

出版商:Akademic-Verlag    

年代:1988

数据来源: Taylor

摘要:

The present paper is concerned with optimization problems in which the data are differentiate functions having a locally Lipschitzian gradient mapping (C1.1-functions). We give second-order sufficient conditions for a stationary solution to be isolated or to be a strict local minimizer. It is shown that the results and ideas known for the case of twice differentiate data can be extended in a natural way. Applications to the analysis of semi-infinite programs, of iterated minimization procedures and of the stability of C1,1-programs are sketched.

ISSN:0233-1934    

DOI:10.1080/02331938808843333

出版商:Akademic-Verlag    

年代:1988

数据来源: Taylor

摘要:

Lehmann, E.: Fallstudien mit dem Computer. B.G. Teubner Stuttgart 1986, 256 S., 58 Abb., DM 24, 80, ISBN 3-519-02537-X.

ISSN:0233-1934    

DOI:10.1080/02331938808843334

出版商:Akademic-Verlag    

年代:1988

数据来源: Taylor

摘要:

We present a branch -and-bound algorithm to minimizef(x) forx∈G∩CwhereGare network flow constraintsis a sum of staircase functions. We minimize the separable staircase functions over a polyhedron making successive linearizations of the objective function. Computational results are presented for the capacitated warehouse location problem.

ISSN:0233-1934    

DOI:10.1080/02331938808843335

出版商:Akademic-Verlag    

年代:1988

数据来源: Taylor

摘要:

Convex-like optimization problems are considered under equality and inequality constraints. For a special ease of [2] a necessary optimality condition is supplied on the Lagrangian.

ISSN:0233-1934    

DOI:10.1080/02331938808843336

出版商:Akademic-Verlag    

年代:1988

数据来源: Taylor

ISSN:0233-1934    

DOI:10.1080/02331938808843337

出版商:Akademic-Verlag    

年代:1988

数据来源: Taylor

摘要:

In the boundary of an-dimensional strong convex set which represents a smooth manifold inEnthe so called affine-geodetical manifolds of different dimension are investigated and some of their global properties are proved. It appeared, that these manifolds are to be considered as the set of all optimal points of certain parametric convex problems.

ISSN:0233-1934    

DOI:10.1080/02331938808843339

出版商:Akademic-Verlag    

年代:1988

数据来源: Taylor

摘要:

Using necessary optimality conditions two different geometrical extremal problems can be formulated as one and the same discrete control problem. This last problem allows a very simple solution by dynamic programming methods

ISSN:0233-1934    

DOI:10.1080/02331938808843340

出版商:Akademic-Verlag    

年代:1988

数据来源: Taylor