Existence of augmented Lagrange multipliers: reduction to exact penalty functions and localization principle

• 成果类型: Article
• 署名作者: Dolgopolik, M. V.
• 署名单位: Saint Petersburg State University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1122-y
• 发表日期: 2017
• 页码: 297-326
• 关键词: saddle-points; optimality conditions; separation approach; Duality; optimization; Penalization; calmness

摘要

In this article, we present new general results on existence of augmented Lagrange multipliers. We define a penalty function associated with an augmented Lagrangian, and prove that, under a certain growth assumption on the augmenting function, an augmented Lagrange multiplier exists if and only if this penalty function is exact. We also develop a new general approach to the study of augmented Lagrange multipliers called the localization principle. The localization principle allows one to study the local behaviour of the augmented Lagrangian near global optimal solutions of the initial optimization problem in order to prove the existence of augmented Lagrange multipliers.