On Blocking and Anti-Blocking Polyhedra in Infinite Dimensions
Abstract: We consider the natural generalizations of blocking and anti-blocking polyhedra in infinite dimensions, and study issues related to duality and integrality of extreme points for these sets. Using appropriate finite truncations, we give conditions under which complementary slackness holds for primal-dual pairs of the infinite linear programming problems associated with infinite blocking and anti-blocking polyhedra. We also give conditions under which the extreme points of infinite blocking and anti-blocking polyhedra are integral. We illustrate an application of our results on an infinite-horizon lot-sizing problem.
Keywords: blocking polyhedron, anti-blocking polyhedron, complementary slackness, integral extreme point
Category 1: Infinite Dimensional Optimization
Category 2: Combinatorial Optimization (Polyhedra )
Category 3: Combinatorial Optimization (Graphs and Matroids )
Citation: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology. November, 2013.
Entry Submitted: 11/18/2013
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