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arXiv · 1903.10137

Multi-objective convex polynomial optimization and semidefinite programming relaxations

Jae Hyoung Lee·Nithirat Sisarat·Liguo Jiao
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Abstract

This paper aims to find efficient solutions to a multi-objective optimization problem (MP) with convex polynomial data. To this end, a hybrid method, which allows us to transform problem (MP) into a scalar convex polynomial optimization problem (P$_z$) and does not destroy the properties of convexity, is considered. First, we show an existence result for efficient solutions to problem (MP) under some mild assumption. Then, for problem (P$_z$), we establish two kinds of representations of non-negativity of convex polynomials over convex semi-algebraic sets, and propose two kinds of finite convergence results of the Lasserre-type hierarchy of semidefinite programming relaxations for problem (P$_z$) under suitable assumptions. Finally, we show that finding efficient solutions to problem (MP) can be achieved successfully by solving hierarchies of semidefinite programming relaxations and checking a flat truncation condition.

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Jae Hyoung Lee, Nithirat Sisarat, Liguo Jiao. 2019-03-25. Multi-objective convex polynomial optimization and semidefinite programming relaxations. https://arxiv.org/abs/1903.10137

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