Utopia point method based robust vector polynomial optimization scheme
Tianyi Han (1), Liguo Jiao (2), Jae Hyoung Lee (3), Junping Yin (2,, 4, 5) ((1) School of Mathematical Sciences, Shanghai Jiao Tong University,, Shanghai, China, (2) Academy for Advanced Interdisciplinary Studies,, Northeast Normal University, Changchun, China
TL;DR
This paper introduces a novel robust vector polynomial optimization scheme that combines the utopia point method with joint+marginal relaxation, addressing non-convex problems effectively.
Contribution
It develops a new approach integrating nonlinear scalarization and relaxation techniques for solving non-convex robust vector polynomial optimization problems.
Findings
Successfully solves RVPOP without convexity assumptions
Provides theoretical analysis of the method
Demonstrates computational effectiveness
Abstract
In this paper, we focus on a class of robust vector polynomial optimization problems (RVPOP in short) without any convex assumptions. By combining/improving the utopia point method (a nonlinear scalarization) for vector optimization and "joint+marginal" relaxation method for polynomial optimization, we solve the RVPOP successfully. Both theoratical and computational aspects are considered.
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Taxonomy
TopicsAdvanced Optimization Algorithms Research · Optimization and Variational Analysis · Fractional Differential Equations Solutions