Optimality conditions and global convergence for nonlinear semidefinite programming

Autor(es)

Andreani, Roberto ^[1] ; Haeser, Gabriel ^[2] ; Viana, Daiana S. ^{[3, 2]}

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Appl Math, Campinas, SP - Brazil

^[2] Univ Sao Paulo, Dept Appl Math, Sao Paulo, SP - Brazil

^[3] Univ Fed Acre, Ctr Exact & Technol Sci, Rio Branco, AC - Brazil

• Tipo de documento: Artigo Científico
• Fonte: MATHEMATICAL PROGRAMMING; v. 180, n. 1-2, p. 203-235, MAR 2020.
• Citações Web of Science: 1

Resumo

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. (AU)

• Processo FAPESP: 17/18308-2 - Condições de otimalidade e algoritmos de segunda-ordem
• Beneficiário: Gabriel Haeser
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 13/05475-7 - Métodos computacionais de otimização
• Beneficiário: Sandra Augusta Santos
• Modalidade de apoio: Auxílio à Pesquisa - Temático