Optimality conditions and global convergence for nonlinear semidefinite programming

作     者：Andreani, Roberto Haeser, Gabriel Viana, Daiana S. 

作者机构：Univ Estadual Campinas Dept Appl Math Campinas SP Brazil Univ Sao Paulo Dept Appl Math Sao Paulo SP Brazil Univ Fed Acre Ctr Exact & Technol Sci Rio Branco AC Brazil 

出 版 物：《MATHEMATICAL PROGRAMMING》 (数学规划)

年 卷 期：2020年第180卷第1-2期

页      面：203-235页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0835[工学-软件工程] 0701[理学-数学] 

基　　金：FAPESP [2013/05475-7, 2017/18308-2] CNPq CAPES Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) [17/18308-2, 13/05475-7] Funding Source: FAPESP 

主　　题：Nonlinear semidefinite programming Optimality conditions Constraint qualifications Practical algorithms 

摘      要：Sequential optimality conditions have played a major role in unifying and extending global convergence results for several classes of algorithms for general nonlinear optimization. In this paper, we extend theses concepts for nonlinear semidefinite programming. We define two sequential optimality conditions for nonlinear semidefinite programming. The first is a natural extension of the so-called Approximate-Karush-Kuhn-Tucker (AKKT), well known in nonlinear optimization. The second one, called Trace-AKKT, is more natural in the context of semidefinite programming as the computation of eigenvalues is avoided. We propose an augmented Lagrangian algorithm that generates these types of sequences and new constraint qualifications are proposed, weaker than previously considered ones, which are sufficient for the global convergence of the algorithm to a stationary point.