Combining trust region and linesearch algorithm for equality constrained optimization

Authors:
Zhensheng Yu;Changyu Wang;Jiguo Yu
Affiliations:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China;Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China and Institute of Operations Research of Qufu Normal University, Qufu, 273165, P. R. China;Department of Computer of Qufu Normal University, Qufu, 273165, P. R. China
Venue:
Journal of Applied Mathematics and Computing
Year:
1986

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Abstract

In this paper, a combining trust region and line search algorithm for equality constrained optimization is proposed. At each iteration, we only need to solve the trust region subproblem once, when the trust region trial step can not be accepted, we switch to line search to obtain the next iteration. Hence, the difficulty of repeated solving trust region subproblem in an iterate is avoided. In order to allow the direction of negative curvature, we add second correction step in trust region step and employ nonmonotone technique in line search. The global convergence and local superlinearly rate are established under certain assumptions. Some numerical examples are given to illustrate the efficiency of the proposed algorithm.