Sensitivity analysis of optimization problems under second order regular constraints

• 成果类型: Article
• 署名作者: Bonnans, JF; Cominetti, R; Shapiro, A
• 署名单位: Universidad de Chile; University System of Georgia; Georgia Institute of Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.23.4.806
• 发表日期: 1998
• 页码: 806-831
• 关键词: banach-spaces; perturbed optimization; nonlinear programs; tangent sets; qualification; projection; STABILITY

摘要

We present a perturbation theory for finite dimensional optimization problems subject to abstract constraints satisfying a second order regularity condition. This is a technical condition that is always satisfied in the case of semi-definite optimization. We derive Lipschitz and Holder expansions of approximate optimal solutions, under a directional constraint qualification hypothesis and various second order sufficient conditions that take into account the curvature of the set defining the constraints of the problem. We show how the theory applies to semi-infinite programs in which the contact set is a smooth manifold and the quadratic growth condition in the constraint space holds, and discuss the differentiability of metric projections as well as the Moreau-Yosida regularization. Finally we show how the theory applies to semi-definite optimization.