Recent Advances In Nonsmooth Optimization

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Ding-zhu Du, Frank Kwang-ming Hwang, Li-qun Qi, Robert S Womersley
World Scientific, Sep 20, 1995 - Mathematics - 480 pages
Nonsmooth 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

Hybrid Methods for Finding the Nearest Euclidean Distance Matrix
1
Subdifferential Characterization of Convexity
18
A Simple Triangulation of Rn with Fewer Simplices for Solving Nonsmooth Convex Programming
24
On Generalized Differentiability of Optimal Solutions and its Application to an Algorithm for Solving Bilevel Optimization Problems
36
Projected Gradient Methods for Nonlinear Complementarity Problems via Normal Maps
57
An NCPFunction and its Use for the Solution of Complementarity Problems
88
An Elementary Rate of Convergence Proof for the Deep Cut Ellipsoid Algorithm
106
Solving Nonsmooth Equations by Means of QuasiNewton Methods with Globalization
121
Generalized Convexity and Higher Order Duality of the Nonlinear Programming Problem with Nonnegative Variables
224
Prederivatives and Second Order Conditions for Infinite Optimization Problems
244
Necessary and Sufficient Conditions for Solution Stability of Parametric Nonsmooth Equations
261
Applications in Nonsmooth Analysis
289
SecondOrder Nonsmooth Analysis in Nonlinear Programming
322
Characterizations of Optimality for Homogeneous Programming Problems with Applications
351
On Regularized Duality In Convex Optimization
381
An Interior Point Method for Solving a Class of LinearQuadratic Stochastic Programming Problems
392

Superlinear Convergence of Approximate Newton Methods for LC1 Optimization Problems without Strict Complementarity
141
On SecondOrder Directional Derivatives in Nonsmooth Optimization
159
On the Solution of Optimum Design Problems with Variational Inequalities
172
Monotonicity and Quasimonotonicity in Nonsmooth Analysis
193
Sensitivity of Solutions in Nonlinear Programming Problems with Nonunique Multipliers
215
A Globally Convergent Newton Method for Solving Variational Inequality Problems with Inequality Constraints
405
Upper Bounds on a Parabolic Second Order Directional Derivative of the Marginal Function
418
A SLP Method with a Quadratic Correction Step for Nonsmooth Optimization
438
A Successive Approximation QuasiNewton Process for Nonlinear Complementarity Problem
459
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