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• W43510049 abstract "We present a faster exponential-time algorithm for integer optimization over quasi-convex polynomials. We study the minimization of a quasiconvex polynomial subject to s quasi-convex polynomial constraints and integrality constraints for all variables. The new algorithm is an improvement upon the best known algorithm due to Heinz (Journal of Complexity, 2005). A lower time complexity is reached through applying a stronger ellipsoid rounding method and applying a recent advancement in the shortest vector problem to give a smaller exponential-time complexity of a Lenstra-type algorithm. For the bounded case, our algorithm attains a time-complexity of s(rlMd) O(1) 2 2n log2(n)+O(n) when M is a bound on the number of monomials in each polynomial and r is the binary encoding length of a bound on the feasible region. In the general case, sl O(1) d O(n) 2 2n log2(n) . In each we assume d 2 is a bound on the total degree of the polynomials and l bounds the maximum binary encoding size of the input." @default.
• W43510049 created "2016-06-24" @default.
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• W43510049 date "2010-06-23" @default.
• W43510049 modified "2023-09-27" @default.
• W43510049 title "A Faster Algorithm for Quasi-convex Integer Polynomial Optimization" @default.
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