A Shadow Simplex Method for Infinite Linear Programs
Operations Research
Integer quadratic quasi-polyhedra
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
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This paper presents a unified treatment of two new simplex-like methods for linear semi-infinite programming problems with quasi-polyhedral feasible sets. The simplex method combines a purification phase I (which provides an extreme point from a given feasible solution) with the iterative application of a pivot operation, yielding a trajectory which consists of a (possibly infinite) sequence of linked edges (phase II). The reduced gradient method also consists of two phases and it can be applied even when the feasible set has no extreme point.