Recent Advances In Nonsmooth Optimization

Ding-zhu Du, Frank Kwang-ming Hwang, Li-qun Qi

• Publisher: World Scientific
• Year: 1995
• Print ISBN: 9789810222659, 9789810222659
• eBook ISBN: 9789812812827
• Topic: Mathematik
• Subtopic: Lineare & nichtlineare Programmierung

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.

Table of contents

• Contents
• Preface
• Hybrid Methods for Finding the Nearest Euclidean Distance Matrix
• Subdifferential Characterization of Convexity
• A Simple Triangulation of Rn with Fewer Simplices for Solving Nonsmooth Convex Programming
• On Generalized Differentiability of Optimal Solutions and its Application to an Algorithm for Solving Bilevel Optimization Problems
• Projected Gradient Methods for Nonlinear Complementarity Problems via Normal Maps
• An NCP–Function and its Use for the Solution of Complementarity Problems
• An Elementary Rate of Convergence Proof for the Deep Cut Ellipsoid Algorithm
• Solving Nonsmooth Equations by Means of Quasi-Newton Methods with Globalization
• Superlinear Convergence of Approximate Newton Methods for LC1 Optimization Problems without Strict Complementarity
• On Second-Order Directional Derivatives in Nonsmooth Optimization
• On the Solution of Optimum Design Problems with Variational Inequalities
• Monotonicity and Quasimonotonicity in Nonsmooth Analysis
• Sensitivity of Solutions in Nonlinear Programming Problems with Nonunique Multipliers
• Generalized Convexity and Higher Order Duality of the Non-linear Programming Problem with Non-negative Variables
• Prederivatives and Second Order Conditions for Infinite Optimization Problems
• Necessary and Sufficient Conditions for Solution Stability of Parametric Nonsmooth Equations
• Miscellaneous Incidences of Convergence Theories in Optimization and Nonlinear Analysis, Part II : Applications in Nonsmooth Analysis
• Second-Order Nonsmooth Analysis in Nonlinear Programming
• Characterizations of Optimality for Homogeneous Programming Problems with Applications
• On Regularized Duality In Convex Optimization
• An Interior Point Method for Solving a Class of Linear-Quadratic Stochastic Programming Problems
• A Globally Convergent Newton Method for Solving Variational Inequality Problems with Inequality Constraints
• Upper Bounds on a Parabolic Second Order Directional Derivative of the Marginal Function
• A SLP Method with a Quadratic Correction Step for Nonsmooth Optimization
• A Successive Approximation Quasi-Newton Process for Nonlinear Complementarity Problem