Nonlinear Programming 2 - 1st Edition - ISBN: 9780124686502, 9781483260419

Nonlinear Programming 2

1st Edition

Proceedings of the Special Interest Group on Mathematical Programming Symposium Conducted by the Computer Sciences Department at the University of Wisconsin - Madison, April 15-17, 1974

Editors: O. L. Mangasarian R. R. Meyer S. M. Robinson
eBook ISBN: 9781483260419
Imprint: Academic Press
Published Date: 28th January 1975
Page Count: 372
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Nonlinear Programming 2 covers the proceedings of the Special Interest Group on Mathematical Programming Symposium conducted by the Computer Sciences Department at the University of Wisconsin, Madison, on April 15-17, 1974.

This book is divided into 13 chapters and begins with a survey of the global and superlinear convergence of a class of algorithms obtained by imposing changing bounds on the variables of the problem. The succeeding chapters deal with the convergence of the well-known reduced gradient method under suitable conditions and a superlinearly convergent quasi-Newton method for unconstrained minimization. These topics are followed by discussion of a superlinearly convergent algorithm for linearly constrained optimization problems and the effective methods for constrained optimization, namely the method of augmented Lagrangians. Other chapters explore a method for handling minimization problems with discontinuous derivatives and the advantages of factorizations of updating for Jacobian-related matrices in minimization problems. The last chapters present the Newton-like methods for the solution of nonlinear equations and inequalities, along with the various aspects of integer programming.

This book will prove useful to mathematicians and computer scientists.

Table of Contents



Convergence Properties of a Class of Minimization Algorithms

Convergence of the Reduced Gradient Method

A Quasi-Newton Method for Unconstrained Minimization Problems

Superlinearly Convergent Algorithms for Linearly Constrained Optimization

An Ideal Penalty Function for Constrained Optimization

On Penalty and Multiplier Methods for Constrained Minimization

Rate of Convergence of the Method of Multipliers with Inexact Minimization

Optimization with Corners

The Use of Matrix Factorizations in Derivative-Free Nonlinear Least Squares Algorithms

Newton Derived Methods for Nonlinear Equations and Inequalities

Disjunctive Programming: Cutting Planes from Logical Conditions

A Generalization of a Theorem of Chvátal and Gomory

Zero-One Zero-One Programming and Enumeration

Subject Index


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© Academic Press 1975
Academic Press
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About the Editor

O. L. Mangasarian

R. R. Meyer

S. M. Robinson

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