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

Peng Wang, Detong Zhu () and Yufeng Song ()
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Peng Wang: Mathematics and Statistics College, Hainan Normal University, Hainan 570203, P. R. China
Detong Zhu: Mathematics and Science College, Shanghai Normal University, Shanghai 200234, P. R. China
Yufeng Song: Institute of Tropical Agriculture and Forestry, Hainan University, Hainan 570203, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2019, vol. 36, issue 03, 1-15

Abstract: 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 (P). 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.

Keywords: Multiobjective optimization; derivative-free optimization; linear programming; backtracking search; linear polynomial interpolation (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S021759591950012X

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