The product of a Gâteaux differentiability space and a separable space is a Gâteaux differentiability space

This paper shows that the product of a Gâteaux differentiability space and a separable Banach space is again a Gâteaux differentiability space.

     

Analysis of Bounds for Multilinear Functions

We analyze four bounding schemes for multilinear functions and theoretically compare their tightness. We prove that one of the four schemes provides the convex envelope and that two schemes provide the concave envelope for the product of p variables over .     

Upper Subderivatives and Generalized Gradients of the Marginal Function of a Non-Lipschitzian Program

We obtain an upper bound for the upper subderivative of the marginal function of an abstract parametric optimization problem when the objective function is lower semicontinuous. Moreover, we apply the result to a nonlinear program with right-hand side perturbations. As a result, we obtain an upper bound for the upper subderivative of the marginal function of a nonlinear program with right-hand side perturbations, which is expressed in dual form in terms of appropriate Lagrange multipliers. Finally, we present conditions which imply that the marginal function is locally Lipschitzian.     

Negative Answer to the Conjecture on the Convexity of the Greatest Eigenvalue

In this note, we show by a counterexample that the conjecture of Seeger on the convexity of the greatest eigenvalue of a real symmetric matrix-valued function does not hold.     

On the Distance between Convex Bodies

ForanytwoconvexbodiesCandDlntheEuc1ideanspaceR"denotebyd(C,D)theminimalnumberAsuchthatthereexistsanaffineoperatorAwhichsatisfiesA(C)=D=AA(C),whereAA(C)denotesahomotheticcopyofA(C)withhom0thetycentrelnsomepointofA(C).d(C,D)iscalledtheMinkowskid1stancebetweenCandD.JohnL'jprovedthatifCisanellipsoid,thend(C,D)相似文献   

广义的Arrow-Barankin-Blackwell定理

本文首次引进了凸锥广义基的概念,然后将局部凸空间的Ａｒｒｏｗ－Ｂａｒａｎｋｉｎ－Ｂｌａｃｋｗｅｌｌ定理推广了到序凸锥为非点式锥的情况。     

The limiting Lagrangian as a consequence of Helly's theorem

The perturbational Lagrangian equation established by Jeroslow in convex semi-infinite programming is derived from Helly's theorem and some prior results on one-dimensional perturbations of convex programs.This research was partially supported by NRC, Grant No. A-4493.     

An application of Guignard's generalized Kuhn-Tucker conditions

Necessary conditions are given for a real-valued function to have a minimum subject to an inequality constraint. Under the appropriate hypotheses, the problem is demonstrated to be a special case of the type of problem to which Guignard's Kuhn-Tucker theorem can be applied.     

An extension of Karmarkar's projective algorithm for convex quadratic programming

We present an extension of Karmarkar's linear programming algorithm for solving a more general group of optimization problems: convex quadratic programs. This extension is based on the iterated application of the objective augmentation and the projective transformation, followed by optimization over an inscribing ellipsoid centered at the current solution. It creates a sequence of interior feasible points that converge to the optimal feasible solution in O(Ln) iterations; each iteration can be computed in O(Ln ³) arithmetic operations, wheren is the number of variables andL is the number of bits in the input. In this paper, we emphasize its convergence property, practical efficiency, and relation to the ellipsoid method.