A subspace SQP method for equality constrained optimization

In this paper, we present a subspace method for solving large scale nonlinear equality constrained optimization problems. The proposed method is based on a SQP method combined with the limited-memory BFGS update formula. Each subproblem is solved in a theoretically suitable subspace. In the case of...

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Bibliographic Details
Published in:Computational optimization and applications 2019-09, Vol.74 (1), p.177-194
Main Authors: Lee, Jae Hwa, Jung, Yoon Mo, Yuan, Ya-xiang, Yun, Sangwoon
Format: Article
Language:English
Subjects:
Constraints
Convex and Discrete Geometry
Management Science
Mathematical models
Mathematics
Mathematics and Statistics
Operations Research
Operations Research/Decision Theory
Optimization
Penalty function
Statistics
Subspace methods
Subspaces
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Summary:In this paper, we present a subspace method for solving large scale nonlinear equality constrained optimization problems. The proposed method is based on a SQP method combined with the limited-memory BFGS update formula. Each subproblem is solved in a theoretically suitable subspace. In the case of few constraints, we show that our search direction in the subspace is equivalent to that of the SQP subproblem in the full space. In the case of many constraints, we reduce the number of constraints in the subproblem and we show that the solution of the subspace subproblem is a descent direction of a particular exact penalty function. Global convergence properties of the proposed method are given for both cases. Numerical results are given to illustrate the soundness of the proposed model.
ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-019-00109-6