Nonsmooth Optimization: Proceedings of a IIASA Workshop, March 28 - April 8, 1977

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Claude Lemarechal, Robert Mifflin
Elsevier, May 19, 2014 - Technology & Engineering - 194 pages
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Nonsmooth Optimization contains the proceedings of a workshop on non-smooth optimization (NSO) held from March 28 to April 8,1977 in Austria under the auspices of the International Institute for Applied Systems Analysis. The papers explore the techniques and theory of NSO and cover topics ranging from systems of inequalities to smooth approximation of non-smooth functions, as well as quadratic programming and line searches.

Comprised of nine chapters, this volume begins with a survey of Soviet research on subgradient optimization carried out since 1962, followed by a discussion on rates of convergence in subgradient optimization. The reader is then introduced to the method of subgradient optimization in an abstract setting and the minimal hypotheses required to ensure convergence; NSO and nonlinear programming; and bundle methods in NSO. A feasible descent algorithm for linearly constrained least squares problems is described. The book also considers sufficient minimization of piecewise-linear univariate functions before concluding with a description of the method of parametric decomposition in mathematical programming.

This monograph will be of interest to mathematicians and mathematics students.
 

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Contents

INTRODUCTION
1
A SURVEY OF SOVIET RESEARCH
5
CHAPTER 2 NONDIFFERENTIABLE OPTIMIZATION AND THE RELAXATION METHOD
31
CHAPTER 3 AN EXTENSION OF THE METHOD OF SUBGRADIENTS
51
CHAPTER 4 NONSMOOTH OPTIMIZATION AND NONLINEAR PROGRAMMING
71
CHAPTER 5 BUNDLE METHODS IN NONSMOOTH OPTIMIZATION
79
CHAPTER 6 A FEASIBLE DESCENT ALGORITHM FOR LINEARLY CONSTRAINED LEAST SQUARES PROBLEMS
103
CHAPTER 7 SUFFICIENT MINIMIZATION OF PIECEWISELINEAR UNIVARIATE FUNCTIONS
127
THE NONCONVEX CASE
131
CHAPTER 9 A SET OF NONSMOOTH OPTIMIZATION TEST PROBLEMS
151
BIBLIOGRAPHY
167
APPENDIX LIST OF PARTICIPANTS
185
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