## Recent Advances in Nonsmooth OptimizationNonsmooth optimization covers the minimization or maximization of functions which do not have the differentiability properties required by classical methods. The field of nonsmooth optimization is significant, not only because of the existence of nondifferentiable functions arising directly in applications, but also because several important methods for solving difficult smooth problems lead directly to the need to solve nonsmooth problems, which are either smaller in dimension or simpler in structure.This book contains twenty five papers written by forty six authors from twenty countries in five continents. It includes papers on theory, algorithms and applications for problems with first-order nondifferentiability (the usual sense of nonsmooth optimization) second-order nondifferentiability, nonsmooth equations, nonsmooth variational inequalities and other problems related to nonsmooth optimization. |

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### Contents

Subdifferential Characterization of Convexity | 18 |

On Generalized Differentiability of Optimal Solutions and its Application | 36 |

Projected Gradient Methods for Nonlinear Complementarity Problems | 57 |

An NCPFunction and its Use for the Solution of Complementarity | 88 |

An Elementary Rate of Convergence Proof for the Deep | 106 |

Solving Nonsmooth Equations by Means of QuasiNewton Methods | 121 |

Superlinear Convergence of Approximate Newton Methods for | 141 |

On SecondOrder Directional Derivatives in Nonsmooth Optimization | 159 |

Necessary and Sufficient Conditions for Solution Stability | 261 |

4 | 264 |

Miscellaneous Incidences of Convergence Theories in Optimization | 289 |

SecondOrder Nonsmooth Analysis in Nonlinear Programming | 322 |

Characterizations of Optimality for Homogeneous Programming | 351 |

On Regularized Duality in Convex Optimization | 381 |

A Globally Convergent Newton Method for Solving Variational | 405 |

Upper Bounds on a Parabolic Second Order Directional Derivative | 418 |

On the Solution of Optimum Design Problems with Variational | 172 |

Monotonicity and Quasimonotonicity in Nonsmooth Analysis | 193 |

VIPI | 215 |

6 | 229 |

Prederivatives and Second Order Conditions for Infinite | 244 |

A SLP Method with a Quadratic Correction Step for Nonsmooth | 438 |

3 | 444 |

A Successive Approximation QuasiNewton Process for Nonlinear | 459 |

### Other editions - View all

Recent Advances in Nonsmooth Optimization Ding-Zhu Du,Liqun Qi,Robert S Womersley Limited preview - 1995 |

### Common terms and phrases

algorithm Applications approximation assume assumption Banach space bounded compact complementarity problem computational consider constraint qualification convex functions convex set defined denote df(x dg(x directional derivative duality epi-derivative equivalent Euclidean distance matrix Example exists feasible finite Frechet function g global convergence gradient Hence holds implies iteration Lemma linear Lipschitz Lipschitz continuous Lipschitzian lower semicontinuous Mathematical Programming Mathematical Society Mathematics of Operations matrix minimization Minkowski gauge monotone multifunction neighborhood Newton method nonempty nonlinear complementarity problem nonlinear programming nonnegative nonsmooth analysis Nonsmooth Optimization normal cone objective function obtain optimal solution optimality conditions optimization problems parametric Penot polyhedral function positively homogeneous Preprint problem P(c programming problems Proof properties Proposition quadratic quasi-Newton methods R. T. Rockafellar result satisfied second order second-order sequence SIAM Journal solving stability step subdifferential subgradient sublinear function subset sufficient condition superlinear Theorem 3.1 theory topology variational inequality vector zero