A subspace SQP method for equality constrained optimization

Jae Hwa Lee (), Yoon Mo Jung (), Ya-xiang Yuan () and Sangwoon Yun ()
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Jae Hwa Lee: Sungkyunkwan University
Yoon Mo Jung: Sungkyunkwan University
Ya-xiang Yuan: ICMSEC, AMSS, CAS
Sangwoon Yun: Sungkyunkwan University

Computational Optimization and Applications, 2019, vol. 74, issue 1, No 7, 177-194

Abstract: Abstract 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.

Keywords: Equality constrained optimization; SQP method; Large scale problems; Subspace techniques; Damped limited-memory BFGS update; 90C30; 90C55; 90C06; 65K05 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10589-019-00109-6

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