Subgradients of marginal functions in parametric mathematical programming

• 成果类型: Article; Proceedings Paper
• 署名作者: Mordukhovich, B. S.; Nam, N. M.; Yen, N. D.
• 署名单位: Wayne State University; Vietnam Academy of Science & Technology (VAST)
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-007-0120-x
• 发表日期: 2009
• 页码: 369-396
• 关键词: lagrange multipliers; STABILITY; convex

摘要

In this paper we derive new results for computing and estimating the so-called Frechet and limiting (basic and singular) subgradients of marginal functions in real Banach spaces and specify these results for important classes of problems in parametric optimization with smooth and nonsmooth data. Then we employ them to establish new calculus rules of generalized differentiation as well as efficient conditions for Lipschitzian stability and optimality in nonlinear and nondifferentiable programming and for mathematical programs with equilibrium constraints. We compare the results derived via our dual-space approach with some known estimates and optimality conditions obtained mostly via primal-space developments.