Recent Advances in Nonsmooth Optimization

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World Scientific, 1995 - Mathematics - 472 pages
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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

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
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