2022/10/31 by Yuya Yamakawa, Yamakawa, Yuya
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2210.17169
openalex publication_date 2022/10/31 · openalex created_date 2022/11/06 · openalex updated_date 2026/07/28
In this paper, we present a stabilized sequential quadratic semidefinite programming (SQSDP) method for nonlinear semidefinite programming (NSDP) problems and prove its local convergence. The stabilized SQSDP method is originally developed to solve degenerate NSDP problems and is based on the stabilized sequential programming (SQP) methods for nonlinear programming (NLP) problems. Although some SQP-type methods for NSDP problems have been proposed, most of them are SQSDP methods which are based on the SQP methods for NLP problems, and there are few researches regarding the stabilized SQSDP methods. In particular, there is room for the development of locally fast convergent stabilized SQSDP methods. We prove not only superlinear but also quadratic convergence of the proposed method under some mild assumptions, such as strict Robinson's constraint qualification and second-order sufficient condition.