3/28/2023 0 Comments Vector td close hard weak![]() Journal of Mathematical Analysis and Applications 2001, 258(1):110–130. Henrion R, Outrata J: A subdifferential condition for calmness of multifunctions. Presented at the IIASA Workshop on Generalized Lagrangians and Their Applications, IIASA, Laxenburg, Austria, 1979 Polyak BT: Sharp Minima, Institue of Control Sciences Lecture Notes. ![]() Computer Sciences Department, University of Wisconsin, Madison, Wis, USA June 1988. ![]() We also give an example to illustrate the optimality condition.įerris MC: Weak sharp minima and penalty functions in mathematical programming. In Section 3, we present a sufficient and necessary condition for weak -sharp local minimizer of vector-valued optimization problems. In Section 2, we recall the definitions of the local Pareto minimizer and weak -sharp local minimizer for vector-valued optimization problems. In addition, we develop the characterization of weak -sharp minima in terms of a nonlinear scalarization function. In this paper, motivated by the work in, we present a sufficient and necessary condition of which a point is a weak -sharp minimum for a vector-valued mapping in the infinite-dimensional spaces. They are a generalization of the weak sharp local minimum of order. Though the notions in are different for vector optimization problems, they are equivalent for scalar optimization problems. In, Studniarski gave the definition of weak -sharp local Pareto minimum in vector optimization problems under the assumption that the order cone is convex and presented necessary and sufficient conditions under a variety of conditions. In, Bednarczuk discussed the weak sharp solution set to vector optimization problems and presented some properties in terms of well-posedness of vector optimization problems. Most recently, Bednarczuk defined weak sharp minima of order for vector-valued mappings under an assumption that the order cone is closed, convex, and pointed and used the concept to prove upper Hölderness and Hölder calmness of the solution set-valued mappings for a parametric vector optimization problem. Recently, the study of weak sharp solution set covers real-valued optimization problems and piecewise linear multiobjective optimization problems. Weak sharp minima play important roles in the sensitivity analysis and convergence analysis of a wide range of optimization algorithms. The notion of a weak sharp minimum in general mathematical program problems was first introduced by Ferris in. ![]()
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