A lift-and-project cutting plane algorithm for mixed 0-1 programs
Mathematical Programming: Series A and B
Discrete Applied Mathematics
Finding an interior point in the optimal face of linear programs
Mathematical Programming: Series A and B
Generalized &agr;-valid cut procedure for concave minimization
Journal of Optimization Theory and Applications
On Finitely Terminating Branch-and-Bound Algorithms for Some Global Optimization Problems
SIAM Journal on Optimization
Finite Exact Branch-and-Bound Algorithms for Concave Minimization over Polytopes
Journal of Global Optimization
Cone Adaptation Strategies for a Finite and Exact Cutting Plane Algorithm for Concave Minimization
Journal of Global Optimization
Lift-and-project for mixed 0-1 programming: recent progress
Discrete Applied Mathematics
Mathematical Programming: Series A and B
Journal of Global Optimization
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Optimization with multivariate stochastic dominance constraints
Mathematical Programming: Series A and B
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In this paper we study linear optimization problems with a newly introduced concept of multidimensional polyhedral linear second-order stochastic dominance constraints. By using the polyhedral properties of this dominance condition, we present a cutting-surface algorithm and show its finite convergence. The cut generation problem is a difference of convex functions (DC) optimization problem. We exploit the polyhedral structure of this problem to present a novel branch-and-cut algorithm that incorporates concepts from concave minimization and binary integer programming. A linear programming problem is formulated for generating concavity cuts in our case, where the polyhedra are unbounded. We also present duality results for this problem relating the dual multipliers to utility functions, without the need to impose constraint qualifications, which again is possible because of the polyhedral nature of the problem. Numerical examples are presented showing the nature of solutions of our model. (A corrected PDF has been appended to the original.)