-
作者：Qi, Mingyao; Jiang, Ruiwei; Shen, Siqian
作者单位：Tsinghua University; University of Michigan System; University of Michigan
摘要：We study a competitive facility location problem (CFLP), where two firms sequentially open new facilities within their budgets, in order to maximize their market shares of demand that follows a probabilistic choice model. This process is a Stackelberg game and admits a bilevel mixed-integer nonlinear program (MINLP) formulation. We derive an equivalent, single-level MINLP reformulation and exploit the problem structures to derive two valid inequalities based on submodularity and concave overes...
-
作者：Chen, Zhi; Kuhn, Daniel; Wiesemann, Wolfram
作者单位：City University of Hong Kong; Imperial College London
摘要：We provide an exact deterministic reformulation for data-driven, chanceconstrained programs over Wasserstein balls. For individual chance constraints as well as joint chance constraints with right-hand-side uncertainty, our reformulation amounts to a mixed-integer conic program. In the special case of a Wasserstein ball with the 1-norm or the ???-norm, the cone is the nonnegative orthant, and the chance-constrained program can be reformulated as a mixed-integer linear program. Our reformulatio...
-
作者：Chen, Zhongzhu; Fampa, Marcia; Lee, Jon
作者单位：University of Michigan System; University of Michigan; Universidade Federal do Rio de Janeiro
摘要：The maximum-entropy sampling problem is the NP-hard problem of maximizing the (log) determinant of an order-s principal submatrix of a given order n covariance matrix C. Exact algorithms are based on a branch-and-bound framework. The problem has wide applicability in spatial statistics and in particular in environmental monitoring. Probably the best upper bound for the maximum empirically is Anstreicher???s scaled ???linx??? bound. An earlier methodology for potentially improving any upper-bou...
-
作者：London, Palma; Vardi, Shai; Eghbali, Reza; Wierman, Adam
作者单位：California Institute of Technology; Purdue University System; Purdue University; University of California System; University of California Berkeley
摘要：This paper presents a black-box framework for accelerating packing optimization solvers. Our method applies to packing linear programming problems and a family of convex programming problems with linear constraints. The framework is designed for high-dimensional problems, for which the number of variables n is much larger than the number of measurements m. Given an (m x n) problem, we construct a smaller (m x epsilon n) problem, whose solution we use to find an approximation to the optimal sol...
