An affine scaling interior trust-region method combining with nonmonotone line search filter technique for linear inequality constrained minimization. Issue 8 (3rd August 2018)

• Record Type: Journal Article
• Authors: Li, Dan; Zhu, Detong
• Is Part Of: International journal of computer mathematics. Volume 95:Issue 8(2018)
• Page Start: 1494
• Page End: 1526
• Publication Date: 2018-08-03
• Subjects: Nonlinear optimization -- trust-region -- line search -- filter method -- interior point; 49M37 -- 65K05 -- 90C30; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2017.1329530
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: This paper proposes an affine scaling interior trust-region method in association with nonmonotone line search filter technique for solving nonlinear optimization problems subject to linear inequality constraints. Based on a Newton step which is derived from the complementarity conditions of linear inequality constrained optimization, a trust-region subproblem subject only to an ellipsoidal constraint is defined by minimizing a quadratic model with an appropriate quadratic function and scaling matrix. The nonmonotone schemes combining with trust-region strategy and line search filter technique can bring about speeding up the convergence progress in the case of high nonlinear. A new backtracking relevance condition is given which assures global convergence without using the switching condition used in the traditional line search filter technique. The fast local convergence rate of the proposed algorithm is achieved which is not depending on any external restoration procedure. The preliminary numerical experiments are reported to show effectiveness of the proposed algorithm.