## Nonlinear programming theory and methods |

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### Contents

SETS AND FUNCTIONS | 15 |

THE NONLINEAR PROGRAMMING PROBLEM | 36 |

QUASICONVEXITY OF FUNCTIONS AND RELATED | 43 |

Copyright | |

14 other sections not shown

### Common terms and phrases

admissible basis algorithm apply assumption basic variables basis entry criterion bounded called chapter co-convex column components concave constraint qualification contradiction converse convex functions convex set corollary corresponding definition denoted differentiable duality eigenvalue eigenvector equality constraints explicitly quasiconcave explicitly quasiconvex feasible set finite number function defined global minimum point go to Step gt(x halfspace Hence Hoang Tuy holds implies inequality infinite edges KTL conditions Lagrangian level sets linear constraints linear programming lower semicontinuous m-vector function Martos matrix MPSubD NLP problem nonempty nonlinear programming nonnegative objective function open set optimum solution parametric partial derivatives Phase point of p(x polyhedron polytope positive primal problem procedure programming problem Proof pseudoconvex pseudomonotonic px(x quadratic function quadratic programming quasiconvex functions quasimonotonic r-th iteration respect saddle point sequence simplex tableau solving stationary point strictly increasing subset tion tp(x v'Cv vector changes vertex xr vertices xr+1