A Stabilized Sequential Quadratic Programming Method for Optimization Problems in Function Spaces

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

Numerical Functional Analysis and Optimization Pub Date : 2023-04-27 DOI:10.1080/01630563.2023.2178009

Yuya Yamakawa

引用次数: 0

Abstract

Abstract In this paper, we propose a stabilized sequential quadratic programming (SQP) method for optimization problems in function spaces. A form of the problem considered in this paper can widely formulate many types of applications, such as obstacle problems, optimal control problems, and so on. Moreover, the proposed method is based on the existing stabilized SQP method and can find a point satisfying the Karush-Kuhn-Tucker (KKT) or asymptotic KKT conditions. One of the remarkable points is that we prove its global convergence to such a point under some assumptions without any constraint qualifications. In addition, we guarantee that an arbitrary accumulation point generated by the proposed method satisfies the KKT conditions under several additional assumptions. Finally, we report some numerical experiments to examine the effectiveness of the proposed method.

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函数空间优化问题的稳定序列二次规划方法

摘要本文提出了一种求解函数空间优化问题的稳定序列二次规划方法。本文所考虑的一种形式的问题可以广泛地表述许多类型的应用，如障碍问题、最优控制问题等。此外，该方法基于现有的稳定SQP方法，可以找到满足Karush-Kuhn-Tucker（KKT）或渐近KKT条件的点。值得注意的一点是，我们在没有任何约束条件的情况下，在一些假设下证明了它的全局收敛性。此外，我们保证由所提出的方法生成的任意累积点在几个附加假设下满足KKT条件。最后，我们报告了一些数值实验来检验该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Functional Analysis and Optimization 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Numerical Functional Analysis and Optimization is a journal aimed at development and applications of functional analysis and operator-theoretic methods in numerical analysis, optimization and approximation theory, control theory, signal and image processing, inverse and ill-posed problems, applied and computational harmonic analysis, operator equations, and nonlinear functional analysis. Not all high-quality papers within the union of these fields are within the scope of NFAO. Generalizations and abstractions that significantly advance their fields and reinforce the concrete by providing new insight and important results for problems arising from applications are welcome. On the other hand, technical generalizations for their own sake with window dressing about applications, or variants of known results and algorithms, are not suitable for this journal. Numerical Functional Analysis and Optimization publishes about 70 papers per year. It is our current policy to limit consideration to one submitted paper by any author/co-author per two consecutive years. Exception will be made for seminal papers.