Multi-objective convex polynomial optimization and semidefinite programming relaxations

Jae Hyoung Lee (), Nithirat Sisarat () and Liguo Jiao ()
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Jae Hyoung Lee: Pukyong National University
Nithirat Sisarat: Naresuan University
Liguo Jiao: Soochow University

Journal of Global Optimization, 2021, vol. 80, issue 1, No 6, 117-138

Abstract: 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 $$({\mathrm{P}}_{z})$$ ( 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 $$(P_{z})$$ ( 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 $$({\mathrm{P}}_{z})$$ ( 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.

Keywords: Multi-objective optimization; hybrid method; convex polynomial optimization; semidefinite programming; sum-of-squares of polynomials; flat truncation condition; 90C29; 90C22; 90C25; 12D15 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-020-00969-x

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