## Generation of Feasible Descent Directions in Continuous Time Linear Programming |

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### Contents

Introduction | 3 |

Basis Inversion Representation and Pricing | 16 |

Descent and Degeneracy | 34 |

2 other sections not shown

### Common terms and phrases

analog apply assume basic feasible solution basis change basis inversion problem breakpoint effects breakpoint regularity condition breakpoint shift Chapter coefficient column complementary slack considered constraints control theory corresponding CTLP algorithm CTLP descent step CTLP problems define degenerate basic variable degenerate pivoting denote Dirac delta functional distribution terms dual analog dual problem dual representation dual solution equation finite number Implicit Function Theorem introduction length introduction of ifc Laplace transform Lemma linear programming m'th component m'th row nonbasic reduced costs nonbasic variable introductions nonzero Note objective contributions obtained by Perold ordinary LP original nonbasic Perold's analysis piecewise analytic pivot formula previous section primal and dual primal solution proof of Theorem proving optimality representation 3.27 repricing revised solution right hand side Section 4.2 shifted breakpoint simplex method simultaneously introduced solving strong duality sufficiently small Theorem 5.9 vector xr(r xr(t zero