Algorithms for Continuous Optimization: The State of the Art

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Emilio Goiuseppe Spedicato
Springer Science & Business Media, May 31, 1994 - Mathematics - 565 pages
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The NATO Advanced Study Institute on "Algorithms for continuous optimiza tion: the state of the art" was held September 5-18, 1993, at II Ciocco, Barga, Italy. It was attended by 75 students (among them many well known specialists in optimiza tion) from the following countries: Belgium, Brasil, Canada, China, Czech Republic, France, Germany, Greece, Hungary, Italy, Poland, Portugal, Rumania, Spain, Turkey, UK, USA, Venezuela. The lectures were given by 17 well known specialists in the field, from Brasil, China, Germany, Italy, Portugal, Russia, Sweden, UK, USA. Solving continuous optimization problems is a fundamental task in computational mathematics for applications in areas of engineering, economics, chemistry, biology and so on. Most real problems are nonlinear and can be of quite large size. Devel oping efficient algorithms for continuous optimization has been an important field of research in the last 30 years, with much additional impetus provided in the last decade by the availability of very fast and parallel computers. Techniques, like the simplex method, that were already considered fully developed thirty years ago have been thoroughly revised and enormously improved. The aim of this ASI was to present the state of the art in this field. While not all important aspects could be covered in the fifty hours of lectures (for instance multiob jective optimization had to be skipped), we believe that most important topics were presented, many of them by scientists who greatly contributed to their development.
 

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Contents

General Optimally Conditions via a Separation Scheme
1
Linear Equations in Optimisation
25
Generalized and Sparse Least Squares Problems
37
Algorithms for Solving Nonlinear Systems of Equations
81
AN OVERVIEW OF UNCONSTRAINED OPTIMIZATION
109
Nonquadratic Model Methods in Unconstrained Optimization
145
ALGORITHMS FOR GENERAL CONSTRAINED NONLINEAR OPTIMIZATION
169
Exact Penalty Methods
209
A Condensed Introduction to Bundle Methods in Nonsmooth Optimization
357
COMPUTATIONAL METHODS FOR LINEAR PROGRAMMING
383
INFEASIBLE INTERIOR POINT METHODS FOR SOLVING LINEAR PROGRAMS
415
Algorithms for Linear Complementarity Problems
435
A HOMEWORK EXERCISE THE BIGM PROBLEM
475
DETERMINISTIC GLOBAL OPTIMIZATION
481
ON AUTOMATIC DIFFERENTIATION AND CONTINUOUS OPTIMIZATION
501
NEURAL NETWORKS AND UNCONSTRAINED OPTIMIZATION
513

Stable BarrierProjection and BarrierNewton Methods for Linear and Nonlinear Programming
255
a Current Survey
287
ABS Methods for Nonlinear Optimization
333
LIMITATIONS CHALLENGES AND OPPORTUNITIES
531
Subject Index
561
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