An infeasible active-set QP-free algorithm for general nonlinear programming. Issue 5 (4th May 2017)

• Record Type: Journal Article
• Authors: Wang, Hua; Liu, Fuyao; Gu, Chao; Pu, Dingguo
• Is Part Of: International journal of computer mathematics. Volume 94:Issue 5(2017)
• Page Start: 884
• Page End: 901
• Publication Date: 2017-05-04
• Subjects: General nonlinear programming -- QP-free method -- active set -- filter -- global convergence -- superlinear convergence; 90C30 -- 49M37 -- 65K10; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2016.1154947
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: We propose an infeasible active set QP-free algorithm for general constrained optimization in this paper. It starts from an arbitrary initial point. At each iteration, only two or three reduced linear equations with the same coefficients are solved to obtain the search direction. To determine the working set, the method makes use of multipliers from the last iteration, eliminating the need to compute a new estimate, and no additional linear systems are solved to select linear independent constraint gradients. The infeasibility measure and the objective function value are controlled separately by the filter technique. Without the positive definiteness assumption on the Hessian estimate, the sequence generated by the algorithm still globally converges to a Karush-Kuhn-Tucker point. And the algorithm obtains superlinear convergence without the strict complementarity. At last, preliminary numerical results are reported.