## Nonlinear Programming: Sequential Unconstrained Minimization TechniquesA reprint of the original volume, which won the Lanchester Prize awarded by the Operations Research Society of America for the best work of 1968. Although out of print for nearly 15 years, it remains one of the most referenced volumes in the field of mathematical programming. Recent interest in interior point methods generated by Karmarkar's Projective Scaling Algorithm has created a new demand for this book because the methods that have followed from Karmarkar's bear a close resemblance to those described. There is no other source for the theoretical background of the logarithmic barrier function and other classical penalty functions. Analyzes in detail the 'central' or 'dual' trajectory used by modern path following and primal/dual methods for convex and general linear programming. As researchers begin to extend these methods to convex and general nonlinear programming problems, this book will become indispensable to them. |

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### Contents

CL04_ch1 | 1 |

CL04_ch2 | 17 |

CL04_ch3 | 39 |

CL04_ch4 | 53 |

CL04_ch5 | 72 |

CL04_ch6 | 86 |

CL04_ch7 | 113 |

CL04_ch8 | 156 |

CL04_backmatter | 197 |

### Other editions - View all

Nonlinear Programming: Sequential Unconstrained Minimization Techniques Anthony V. Fiacco,Garth P. McCormick No preview available - 1990 |

### Common terms and phrases

applied assumed assumptions auxiliary function bounded compact set computational concave concave function convergence convex function convex programming problem convex set Corollary decreasing defined dual variables equations example exists exterior point algorithms feasible points feasible region finite first-order constraint qualification first-order necessary conditions follows given global gradient hence implies interior point methods inverse isolated trajectory iteration Lagrange multipliers Lagrangian Lemma lime limit point linear programming linearly independent local minimum logarithmic penalty function mathematical programming matrix of second minimize f(x non-negative nonempty nonlinear programming nonzero objective function optimal optimum penalty term point unconstrained minimization problem functions Proof properties proved quadratic form quadratic loss function satisfied second partial derivatives Section solution solve strictly convex sufficient conditions Theorem uncon unconstrained function unconstrained minimization algorithms Unconstrained Minimization Techniques unique vector Whº yields zero