Separations and Optimality of Constrained Multiobjective Optimization via Improvement Sets

Jiawei Chen (), La Huang () and Shengjie Li ()
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Jiawei Chen: Southwest University
La Huang: Southwest University
Shengjie Li: Chongqing University

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 3, No 6, 794-823

Abstract: Abstract In this paper, we investigate the separations and optimality conditions for the optimal solution defined by the improvement set of a constrained multiobjective optimization problem. We introduce a vector-valued regular weak separation function and a scalar weak separation function via a nonlinear scalarization function defined in terms of an improvement set. The nonlinear separation between the image of the multiobjective optimization problem and an improvement set in the image space is established by the scalar weak separation function. Saddle point type optimality conditions for the optimal solution of the multiobjective optimization problem are established, respectively, by the nonlinear and linear separation methods. We also obtain the relationships between the optimal solution and approximate efficient solution of the multiobjective optimization problem. Finally, sufficient and necessary conditions for the (regular) linear separation between the approximate image of the multiobjective optimization problem and a convex cone are also presented.

Keywords: Constrained multiobjective optimization; Image space analysis; Improvement set; Nonlinear separation; Optimality condition; 49K05; 90C29 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-018-1325-2

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