Derivative-Free Feasible Backtracking Search Methods for Nonlinear Multiobjective Optimization with Simple Boundary Constraint

• Published in: Asia-Pacific journal of operational research Vol. 36; no. 3; p. 1950012
• Main Authors: Wang, Peng, Zhu, Detong, Song, Yufeng
• Format: Journal Article
• Language: English
• Published: Singapore World Scientific Publishing Co. Pte., Ltd 01.06.2019
• Subjects: Algorithms; Critical point; Feasibility; Interpolation; Iterative methods; Linear programming; Multiple objective analysis; Operations research; Optimization; Searching
• ISSN: 0217-5959; 1793-7019; 0217-5959
• DOI: 10.1142/S021759591950012X

In this paper, a derivative-free linear feasible direction models with backtracking search technique is considered for solving nonlinear multiobjective optimization problems subject to simple boundary constraint. The algorithm is designed to build linear interpolation models for each function of problem [Formula: see text]. We build the linear programming subproblem using linear interpolation function without the second-order derivative information. The new backtracking search step size function is given in our algorithm which guarantees both the monotone descent property of each function and the feasibility of the iterative point. Under reasonable assumptions, we prove that the algorithm converges to a weakly Pareto critical point of problem. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.