Solving Optimization Problems over the Weakly Efficient Set. (4th December 2021)

• Record Type: Journal Article
• Authors: Sadeghi, Javad; Mohebi, Hossein
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 2(2021)
• Page Start: 180
• Page End: 210
• Publication Date: 2021-12-04
• Subjects: Nonlinear programming -- multiobjective programming -- nonconvex programming -- weak-efficiency -- generalized cutting plane method; 90C26 -- 65K05 -- 90C30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1871009
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, we study the optimization problem ( PWE ) of minimizing a convex function over the set of weakly efficient solutions of a convex multiobjective problem. This is done by using the fact that each lower semicontinuous convex function is an upper envelope of its affine minorants together with a generalized cutting plane method. We give necessary conditions for optimal solutions of the problem ( PWE ) . Moreover, a novel algorithm for solving the problem ( PWE ) together with numerical results are presented. We also prove that the proposed algorithm terminates after a finite numbers of iterations, and the algorithm is coded in MATLAB language and evaluated by numerical examples.