A revised sequential quadratic semidefinite programming method for nonlinear semidefinite optimization
A revised sequential quadratic semidefinite programming method for nonlinear semidefinite optimization
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DOI：
10.3934/jimo.2023019
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发表时间：
2022-04
影响因子：
1.3
通讯作者：
Kosuke Okabe;Yuya Yamakawa;E. H. Fukuda
中科院分区：
文献类型：
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作者：
Kosuke Okabe;Yuya Yamakawa;E. H. Fukuda
在2020年，山川和Okuno提出了一种稳定的顺序二次半足限编程（SQSDP）方法，尤其是退化非线性半际半决赛优化问题。该算法显示在全球范围内无限制地收敛，并且具有一些不错的属性，包括可行的子问题及其可能的不精确计算。特别是，为近似-karush-kuhn-tucker（AKKT）和Trace-Akkt条件建立了收敛性，这是非线性圆锥形上下文的两个顺序最佳条件。但是，最近，还认为互补性 - akkt（CAKKT）条件是以前提到的替代条件，这是更实用的。由于很少有方法表明至少在圆锥优化的情况下会收敛到CAKKT点，并完成与SQSDP相关的研究，因此在这里我们提出了该方法的修订版本，并保持良好的特性。我们修改了先前的算法，证明了CAKKT意义上的全局收敛性，并显示了一些初步的数值实验。
In 2020, Yamakawa and Okuno proposed a stabilized sequential quadratic semidefinite programming (SQSDP) method for solving, in particular, degenerate nonlinear semidefinite optimization problems. The algorithm is shown to converge globally without a constraint qualification, and it has some nice properties, including the feasible subproblems, and their possible inexact computations. In particular, the convergence was established for approximate-Karush-Kuhn-Tucker (AKKT) and trace-AKKT conditions, which are two sequential optimality conditions for the nonlinear conic contexts. However, recently, complementarity-AKKT (CAKKT) conditions were also consider, as an alternative to the previous mentioned ones, that is more practical. Since few methods are shown to converge to CAKKT points, at least in conic optimization, and to complete the study associated to the SQSDP, here we propose a revised version of the method, maintaining the good properties. We modify the previous algorithm, prove the global convergence in the sense of CAKKT, and show some preliminary numerical experiments.