排序方式: 共有49条查询结果,搜索用时 15 毫秒
1.
Juan Enrique Martínez-Legaz 《Optimization》2015,64(1):87-96
This article surveys the main contributions of K.-H. Elster to the theory of generalized conjugate functions and its applications to duality in nonconvex optimization. 相似文献
2.
There are infinitely many ways of representing a d.c. function as a difference of convex functions. In this paper we analyze
how the computational efficiency of a d.c.optimization algorithm depends on the representation we choose for the objective
function, and we address the problem of characterizing and obtaining a computationally optimal representation. We introduce
some theoretical concepts which are necessary for this analysis and report some numerical experiments.
相似文献
3.
Juan Enrique Martínez-Legaz Maxim Ivanov Todorov Carlos Armando Zetina 《Numerical Functional Analysis & Optimization》2014,35(7-9):1078-1094
In this article, we extend the definition of γ-active constraints for linear semi-infinite programming to a definition applicable to convex semi-infinite programming, by two approaches. The first approach entails the use of the subdifferentials of the convex constraints at a point, while the second approach is based on the linearization of the convex inequality system by means of the convex conjugates of the defining functions. By both these methods, we manage to extend the results on γ-active constraints from the linear case to the convex case. 相似文献
4.
We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in the decomposition is requested to be closed), while others are specific of the new family. 相似文献
5.
A. Hantoute J. E. Martínez-Legaz 《Journal of Optimization Theory and Applications》2013,159(3):673-680
We give a necessary and sufficient condition for a difference of convex (DC, for short) functions, defined on a normed space, to be Lipschitz continuous. Our criterion relies on the intersection of the ε-subdifferentials of the involved functions. 相似文献
6.
J. E. Martínez-Legaz 《Mathematical Methods of Operations Research》1983,27(1):257-266
In this article we develop a conjugacy theory in quasiconvex analysis, in which no lower semicontinuity or normality assumption is needed to ensure the coincidence of the second conjugate of any function with its quasivonvex hull. This is made by an extension of the concept ofH-conjugation, and is based on a separation theorem by general halfspaces. The theory is applied in mathematical programming to define dual problems, which consist in maximizing a quasiconcave function of matricial variable, the optimum being always attained. The absence of duality gap is equivalent to the quasiconvexity of the perturbation function at the origin. A Lagrangian for general problems is studied and compared with the one of Luenberger in the case of vertical perturbations. 相似文献
7.
Set-Valued and Variational Analysis - The production correspondence associated with a technology maps every input vector into the set of output vectors that may be obtained by means of those... 相似文献
8.
Nicolas Hadjisavvas Flávia M. O. Jacinto Juan E. Martínez-Legaz 《Set-Valued and Variational Analysis》2016,24(2):323-332
We present necessary and sufficient conditions for a monotone bifunction to be maximally monotone, based on a recent characterization of maximally monotone operators. These conditions state the existence of solutions to equilibrium problems obtained by perturbing the defining bifunction in a suitable way. 相似文献
9.
J.M. Bilbao J.E. Martínez-Legaz 《Journal of Mathematical Analysis and Applications》2012,387(2):1167-1175
We analyze the least increment function, a convex function of n variables associated to an n-person cooperative game. Another convex representation of cooperative games, the indirect function, has previously been studied. At every point the least increment function is greater than or equal to the indirect function, and both functions coincide in the case of convex games, but an example shows that they do not necessarily coincide if the game is totally balanced but not convex. We prove that the least increment function of a game contains all the information of the game if and only if the game is totally balanced. We also give necessary and sufficient conditions for a function to be the least increment function of a game as well as an expression for the core of a game in terms of its least increment function. 相似文献
10.
Given two point to set operators, one of which is maximally monotone, we introduce a new distance in their graphs. This new concept reduces to the classical Bregman distance when both operators are the gradient of a convex function. We study the properties of this new distance and establish its continuity properties. We derive its formula for some particular cases, including the case in which both operators are linear monotone and continuous. We also characterize all bi-functions D for which there exists a convex function h such that D is the Bregman distance induced by h. 相似文献