On second-order Fritz John type optimality conditions in nonsmooth multiobjective programming

• 成果类型: Article; Proceedings Paper
• 署名作者: Gutierrez, C.; Jimenez, B.; Novo, V.
• 署名单位: Universidad Nacional de Educacion a Distancia (UNED); Universidad de Valladolid
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-009-0318-1
• 发表日期: 2010
• 页码: 199-223
• 关键词: differentiable vector optimization; tangent sets; directional-derivatives; minimization problems; banach-spaces; constraints; 1st

摘要

We study a multiobjective optimization program with a feasible set defined by equality constraints and a generalized inequality constraint. We suppose that the functions involved are Fr,chet differentiable and their Fr,chet derivatives are continuous or stable at the point considered. We provide necessary second order optimality conditions and also sufficient conditions via a Fritz John type Lagrange multiplier rule and a set-valued second order directional derivative, in such a way that our sufficient conditions are close to the necessary conditions. Some consequences are obtained for parabolic directionally differentiable functions and C (1,1) functions, in this last case, expressed by means of the second order Clarke subdifferential. Some illustrative examples are also given.