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  • A new approximation hierarchy for polynomial conic optimization
    Dickinson, Peter J. C., 1985- ; Povh, Janez, 1973-
    In this paper we consider polynomial conic optimization problems, where the feasible set is defined by constraints in the form of given polynomial vectors belonging to given nonempty closed convex ... cones, and we assume that all the feasible solutions are non-negative. This family of problems captures in particular polynomial optimization problems (POPs), polynomial semi-definite polynomial optimization problems (PSDPs) and polynomial second-order cone-optimization problems (PSOCPs). We propose a new general hierarchy of linear conic optimization relaxations inspired by an extension of Pólyaʼs Positivstellensatz for homogeneous polynomials being positive over a basic semi-algebraic cone contained in the non-negative orthant, introduced in Dickinson and Povh (J Glob Optim 61(4):615-625, 2015). We prove that based on some classic assumptions, these relaxations converge monotonically to the optimal value of the original problem. Adding a redundant polynomial positive semi-definite constraint to the original problem drastically improves the bounds produced by our method. We provide an extensive list of numerical examples that clearly indicate the advantages and disadvantages of our hierarchy. In particular, in comparison to the classic approach of sum-of-squares, our new method provides reasonable bounds on the optimal value for POPs, and strong bounds for PSDPs and PSOCPs, even outperforming the sum-of-squares approach in these latter two cases.
    Vir: Computational optimization and applications. - ISSN 0926-6003 (Vol. 73, iss. 1, 2019, str. 37-67)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2019
    Jezik - angleški
    COBISS.SI-ID - 16466459

    Povezava(-e):

    https://link.springer.com/article/10.1007%2Fs10589-019-00066-0
    Repozitorij Univerze v Ljubljani – RUL
    DOI

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