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• W3120476505 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 $$({mathrm{P}}_{z})$$ 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 $$({mathrm{P}}_{z})$$ 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." @default.
• W3120476505 created "2021-01-18" @default.
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• W3120476505 date "2021-01-04" @default.
• W3120476505 modified "2023-10-06" @default.
• W3120476505 title "Multi-objective convex polynomial optimization and semidefinite programming relaxations" @default.
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• W3120476505 doi "https://doi.org/10.1007/s10898-020-00969-x" @default.
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