Granularity for Mixed-Integer Polynomial Optimization Problems

Carl Eggen (), Oliver Stein () and Stefan Volkwein ()
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Carl Eggen: University of Konstanz
Oliver Stein: Karlsruhe Institute of Technology (KIT)
Stefan Volkwein: University of Konstanz

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 2, No 3, 24 pages

Abstract: Abstract Finding good feasible points is crucial in mixed-integer programming. For this purpose we combine a sufficient condition for consistency, called granularity, with the moment-/sum-of-squares-hierarchy from polynomial optimization. If the mixed-integer problem is granular, we obtain feasible points by solving continuous polynomial problems and rounding their optimal points. The moment-/sum-of-squares-hierarchy is hereby used to solve those continuous polynomial problems, which generalizes known methods from the literature. Numerical examples from the MINLPLib illustrate our approach.

Keywords: Mixed-integer nonlinear programming; Granularity; Rounding; Polynomial optimization; Semidefinite programming; 90C10; 90C11; 90C22; 90C23; 90C31 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02631-6

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