报告题目：Linear Reformulation of Polynomial Discrete Programming for Fast Computation
报告人：Professor Shu-Cherng Fang
报告人单位：North Carolina State University
摘要：Optimization models involving a polynomial objective function and multiple polynomial constraints with discrete variables are often encountered in engineering, management and systems. Treating the non-convex cross-product terms is the key. State-of-the-art methods usually convert such a problem into a 0-1 mixed integer linear programming problem, and, then, adopt a branch-and-bound scheme to ﬁnd an optimal solution. Much eﬀort has been spent on reducing the required numbers of variables and linear constraints as well as on avoiding unbalanced branch-and-bound trees. This talk presents a novel idea of linearizing the discrete cross-product terms in an extremely eﬀective manner. Theoretical analysis shows that the new method signiﬁcantly reduces the required number of linear constraints from O(h^3n^3) to O(hn) for a cubic polynomial discrete program with n variables in h possible values. Numerical experiments also conﬁrm a two-order (102 times) reduction in computational time for randomly generated problems with millions of variables and constraints.