A method combining norm-relaxed QCQP subproblems with active set identification for inequality constrained optimization. (3rd June 2022)

• Record Type: Journal Article
• Authors: Liu, Mei-xing; Jian, Jin-bao; Tang, Chun-ming
• Is Part Of: Optimization. Volume 71:Number 6(2022)
• Page Start: 1525
• Page End: 1555
• Publication Date: 2022-06-03
• Subjects: Inequality constrained optimization -- SQCQP -- active set identification -- global convergence -- superlinear convergence; 90C30 -- 49M37 -- 65K05; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1818744
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, an adaptation of the sequential quadratically constrained quadratic programming method is proposed to solve inequality constrained minimization. At each iteration, it solves a norm-relaxed quadratically constrained quadratic programming subproblem that uses an active set identification technique to reduce the scale and computational cost. By taking a valid line search, the iterates always get into the feasible set after a finite number of iterations, and followed by a suitable update rule for the penalty parameters. Under suitable conditions without the strict complementarity, our method has the global and superlinear convergence properties. In addition, numerical results are reported to demonstrate the efficiency of the proposed method.