Nonlinear programming 3 [electronic resource] : proceedings of the Special Interest Group on Mathematical Programming symposium / conducted by the Computer Sciences Department at the University of Wisconsin--Madison, July 11-13, 1977 ; edited by Olvi L. Mangasarian, Robert R. Meyer, Stephen M. Robinson.
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| Format: | Electronic Conference Proceeding eBook |
| Language: | English |
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New York :
Academic Press,
1978.
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Table of Contents:
- Front Cover; Nonlinear Programming 3; Copyright Page; Table of Contents; CONTRIBUTORS; PREFACE; CHAPTER 1. MONOTONE OPERATORS AND AUGMENTED LAGRANGIAN METHODS IN NONLINEAR PROGRAMMING; ABSTRACT; 1. INTRODUCTION; 2. MONOTONE OPERATORS AND VARIATIONAL INEQUALITIES; 3. PROXIMAL POINT ALGORITHM FOR MONOTONE OPERATORS; 4. APPLICATION TO CONVEX PROGRAMMING; 5. APPLICATION TO VARIATIONAL INEQUALITIES; REFERENCES; CHAPTER 2. THE CONVERGENCE OF VARIABLE METRIC METHODS FOR NONLINEARLY CONSTRAINED OPTIMIZATION CALCULATIONS; ABSTRACT; 1. INTRODUCTION; 2. SOME CONDITIONS AND THEIR CONSEQUENCES.
- 3. A GENERAL THEOREM EOR SUPERLINEAR CONVERGENCE4. THE DEFINITION OF Bk+1; 5. AN R-SUPERLINEAR CONVERGENCE THEOREM; ACKNOWLEDGMENT; REFERENCES; CHAPTER 3. A HYBRID METHOD FOR NONLINEAR PROGRAMMING; ABSTRACT; 1. INTRODUCTION; 2. THE METHOD; 3. GLOBAL PROPERTIES; 4. LOCAL PROPERTIES; 5. CONCLUSIONS; REFERENCES; CHAPTER 4. TWO-PHASE ALGORITHM FOR NONLINEAR CONSTRAINT PROBLEMS; ABSTRACT; 1. INTRODUCTION; 2. LINEARIZATION OF NONLINEAR CONSTRAINTS; 3. EXTERNAL SQUARED PENALTY; 4. PRACTICAL IMPLEMENTATION; 5. DISCUSSION; REFERENCES.
- CHAPTER 5. QUASI-NEWTON METHODS FOR EQUALITY CONSTRAINED OPTIMIZATION: EQUIVALENCE OF EXISTING METHODS AND A NEW IMPLEMENTATION1. INTRODUCTION; 2. THE MULTIPLIER EXTENSION QUASI-NEWTON METHODS; 3. THE STRUCTURED MULTIPLIER EXTENSION QUASI-NEWTON METHODS; 4. THE MULTIPLIER UPDATE QUASI-NEWTON METHODS; 5. THE BALANCED MULTIPLIER UPDATE QUASI-NEWTON METHODS; 6. THE QUADRATIC PROGRAMMING QUASI-NEWTON METHOD; 7. THE ADDITION OF SUPERSTRUCTURE; 8. THE MULTIPLIER SUBSTITUTION QUASI-NEWTON METHODS; 9. THE STRUCTURED MULTIPLIER SUBSTITUTION QUASI-NEWTON METHODS.
- 10. THE BEST OF THE MULTIPLIER QUASI-NEWTON METHODS11. AN IMPLEMENTATION BASED ON THE SVD; REFERENCES; CHAPTER 6. AN IDEALIZED EXACT PENALTY FUNCTION; ABSTRACT; 1. INTRODUCTION; 2. MOVEMENT OF A PARTICLE UNDER DIFFERENT FORCES; 3. FLETCHER'S EXACT PENALTY FUNCTION (EQUALITY CASE); 4. THE INEQUALITY CONSTRAINED PROBLEM; 5. FLETCHER'S EXACT PENALTY FUNCTION (INEQUALITY CASE); REFERENCES; CHAPTER 7. EXACT PENALTY ALGORITHMS FOR NONLINEAR PROGRAMMING; ABSTRACT; 1. INTRODUCTION; 2. DEFINITIONS AND NOTATIONS; 3. STATIONARY POINTS OF THE EXACT PENALTY FUNCTION AND OPTIMALITY FUNCTIONS.
- 4. DESCRIPTION OF THE ALGORITHM5. RATE OF CONVERGENCE OF THE EXACT PENALTY ALGORITHMS; 6. COMPUTATIONAL RESULTS; 7. ADDITIONAL RESULTS; ACKNOWLEDGMENTS; REFERENCES; CHAPTER 8. A VARIABLE METRIC METHOD FOR LINEARLY CONSTRAINED MINIMIZATION PROBLEMS; 1. INTRODUCTION; 2. GENERAL DESCRIPTION OF THE ALGORITHM; 3. DETAILED STATEMENT OF THE ALGORITHM; 4. SUPERLINEAR CONVERGENCE; REFERENCES; CHAPTER 9. SOLVING SYSTEMS OF NONLINEAR EQUATIONS BY BROYDEN'S METHOD WITH PROJECTED UPDATES; ABSTRACT; 1. INTRODUCTION; 2. THE NEW METHOD; 3. BEHAVIOR ON LINEAR OR PARTLY LINEAR PROBLEMS.