A discrete dynamic convexized method for nonlinear integer programming

Authors:
Wenxing Zhu;Hong Fan
Affiliations:
Center for Discrete Mathematics and Theoretical Computer Science, Fuzhou University, Fuzhou 350002, China;College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper, we consider the box constrained nonlinear integer programming problem. We present an auxiliary function, which has the same discrete global minimizers as the problem. The minimization of the function using a discrete local search method can escape successfully from previously converged discrete local minimizers by taking increasing values of a parameter. We propose an algorithm to find a global minimizer of the box constrained nonlinear integer programming problem. The algorithm minimizes the auxiliary function from random initial points. We prove that the algorithm can converge asymptotically with probability one. Numerical experiments on a set of test problems show that the algorithm is efficient and robust.