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

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,...

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Bibliographic Details
Published inNumerical functional analysis and optimization Vol. 44; no. 9; pp. 867 - 905
Main Author Yamakawa, Yuya
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 04.07.2023
Taylor & Francis Ltd
Subjects
Asymptotic KKT conditions
Asymptotic methods
Banach space
Function space
global convergence
Optimal control
Optimization
PDE constrained optimization
Quadratic programming
stabilized SQP method
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Summary: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.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2023.2178009