## Linear programming in infinite-dimensional spaces: theory and applicationsInfinite-dimensional linear programs; Algebraic fundamentals; Topology and duality. Semi-infinite linear programs; The mass-transfer problem; Maximal flow in a dynamic network; Continuous linear programs; Other infinite linear programs; Index. |

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### Contents

Infinitedimensional Linear Programs | 1 |

Algebraic Fundamentals | 16 |

Topology and Duality | 35 |

Copyright | |

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algebraic dual asymptotically consistent basic feasible solution basic optimal solution basic solutions bounded Chapter choose compact set components consider constr(x constraint map continuous functions continuous linear program convex cone convex hull convex set defined dual pair dual problem duality gap duality result duality theory elements example extreme points feasible set finite linear program finite number finite value follows formulation given Hence infinite infinite-dimensional linear programs Lemma linearly independent Mackey topology matrix maximize maximum-flow problem measure MHEP minimize network-flow problem node non-negative non-zero objective function objective function value piecewise continuous assignment posed positive cone primal and dual primal problem Proof reachable reduced-cost functional Remez exchange algorithm SCLP Section semi-infinite linear programs sequence simplex algorithm simplex extension SIP1 SIP2 solution for LP solvable storage strong duality subset subspace subvalue supp(w Suppose TCNP topology vector spaces weak duality zero