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Christopher Hojny (c.hojnytue.nl) Abstract: Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an integral relaxation polytope, generalizing work by Del Pia and Khajavirad (SIAM Journal on Optimization, 2018) and Buchheim, Crama and RodríguezHeck (European Journal of Operations Research, 2019). We also present an algorithm that finds these extra monomials for a given polynomial to yield an integral relaxation polytope or determines that no such set of extra monomials exists. In the former case, our approach yields an algorithm to solve the given polynomial optimization problem as a compact LP, and we complement this with a purely combinatorial algorithm. Keywords: polynomial optimization, linearization, integer linear programming Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming ) Category 2: Combinatorial Optimization (Polyhedra ) Citation: Download: [PDF] Entry Submitted: 11/15/2019 Modify/Update this entry  
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