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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Peng Wang & Detong Zhu & Yufeng Song, 2019. "Derivative-Free Feasible Backtracking Search Methods for Nonlinear Multiobjective Optimization with Simple Boundary Constraint," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(03), pages 1-15, June.
    • Handle: RePEc:wsi:apjorx:v:36:y:2019:i:03:n:s021759591950012x
    DOI: 10.1142/S021759591950012X
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    References listed on IDEAS

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    1. R. S. Burachik & C. Y. Kaya & M. M. Rizvi, 2014. "A New Scalarization Technique to Approximate Pareto Fronts of Problems with Disconnected Feasible Sets," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 428-446, August.
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