Nonlinear programming 4 : proceedings of the Nonlinear Programming Symposium 4 / / conducted by the Computer Sciences Department at the University of Wisconsin--Madison, July 14-16, 1980 ; edited by Olvi L. Mangasarian, Robert R. Meyer, Stephen M. Robinson

• Record Nr.: UNINA9910806167603321
• Pubbl/distr/stampa: New York, New York ; ; London, [England] : , : Academic Press, , 1981; ©1981
• ISBN: 1-4832-6017-8
• Descrizione fisica: 1 online resource (560 p.)
• Disciplina: 519.7/6
• Soggetti: Nonlinear programming
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index at the end of each chapters.
• Nota di contenuto: Front Cover; Nonlinear Programming 4; Copyright Page; Table of Contents; CONTRIBUTORS; PREFACE; CHAPTER 1. AN UPPER TRIANGULAR MATRIX METHOD FORQUADRATIC PROGRAMMING; ABSTRACT; 1. INTRODUCTION; 2. A COMPARISON OF THREE ACTIVE SET METHODS; 3. THE CALCULATION OF d ANDλ; 4. THE REVISION OF U AND L; 5. DISCUSSION; ACKNOWLEDGMENTS; REFERENCES; CHAPTER 2. SOLVING QUADRATIC PROGRAMSBY AN EXACT PENALTY FUNCTION; ABSTRACT; 1. INTRODUCTION; 2. THE METHOD; 3. BASIC PROPERTIES; 4. FINITE CONVERGENCE; 5. COMPUTATIONAL RESULTS; ACKNOWLEDGMENT; REFERENCES; CHAPTER 3. QP-BASEDMETHODS FOR LARGE-SCALE NONLINEARLY CONSTRAINED OPTIMIZATIONABSTRACT; 1. INTRODUCTION; 2. LARGE-SCALE LINEARLY CONSTRAINED OPTIMIZATION; 3. QP-BASED METHODS FOR DENSE PROBLEMS; 4. THE USE OF A LINEARLY CONSTRAINED SUBPROBLEM; 5. EXTENSION OF QP-BASED METHODS TO THE LARGE-SCALE CASE; 6. REPRESENTING THE BASIS INVERSE; 7. THE SEARCH DIRECTION FOR THE SUPERBASIC VARIABLES; 8. AN INEQUALITY QPAPPROACH; 9. CONCLUSIONS; REFERENCES; CHAPTER 4. NUMERICAL EXPERIMENTS WITH AN EXACT L1PENALTY FUNCTION METHOD; ABSTRACT; 1. INTRODUCTION; 2. A GLOBALLY CONVERGENT ; ALGORITHM; 3. AN ACTIVE SET METHOD4. NUMERICAL EXPERIMENTS AND DISCUSSION; ACKNOWLEDGMENTS; REFERENCES; CHAPTER 5. AN ITERATIVE LINEAR PROGRAMMING ALGORITHMBASED ON AN AUGMENTED LAGRANGIAN; ABSTRACT; REFERENCES; CHAPTER 6. ITERATIVE ALGORITHMSFOR SINGULAR MINIMIZATION PROBLEMS; ABSTRACT; 1. INTRODUCTION; 2. THE QUADRATIC CASE; 3. NONQUADRATIC CASE; 4. MINIMIZATION IN THE PRESENCE OF ERRORS; CONCLUSIONS; ACKNOWLEDGMENTS; REFERENCES; CHAPTER 7. A NEW DERIVATION OF SYMMETRICPOSITIVE DEFINITE SECANT UPDATES; ABSTRACT; 1. INTRODUCTION AND BACKGROUND; 2. THE BFGS AND DFP FROM THE GOOD AND BAD BROYDEN METHODS; 3. HEREDITARY POSITIVE DEFINITENESS AND IREN SIZING FORSYMMETRIC RANK-TWO UPDATES4. A PROJECTED BFGS FROM THE PROJECTED BROYDEN UPDATE; 5. UPDATING CHOLESKY FACTORS; REFERENCES; APPENDIX: THE SCALED BFGS DERIVATION; CHAPTER8. ON PRECONDITIONED CONJUGATE GRADIENT METHODS; ABSTRACT; I. INTRODUCTION; II. USING MODERATE ADDITIONAL STORAGE; III. UTILIZING SPARSE SECOND ORDER INFORMATION; REFERENCES; CHAPTER 9. FINDING THE GLOBAL MINIMUM OF A FUNCTION OF ONE VARIABLE USING THE METHOD OF CONSTANTSIGNED HIGHER ORDER DERIVATIVES; ABSTRACT; 1. INTRODUCTION; 2. PRELIMINARY THEOREMS AND LEMMAS; 3. ALGORITHMIC CONSIDERATIONS4. APPLICATION TO POLYNOMIAL MINIMIZATION; 5. EFFECTS OF CALCULATION ERRORS; 6. COMMENT; REFERENCES; CHAPTER 10. ON A BUNDLE ALGORITHMFOR NONSMOOTH OPTIMIZATION; ABSTRACT; 1. INTRODUCTION; 2. THE ALGORITHM WITHOUT CONSTRAINTS; 3. LINEARLY CONSTRAINED PROBLEMS; APPENDIX; REFERENCES; CHAPTER 11. CONVERGENCE RESULTS IN A CLASS OFVARIABLE METRIC SUBGRADIENT METHODS1; ABSTRACT; 1. INTRODUCTION; 2. EXAMPLES; 3. A CLASS OF VARIABLE METRIC SUBGRADIENT OPTIMIZATIONMETHODS; 4. VARIOUS METHODS; 5. BEHAVIOUR ON SYSTEMS OF LINEAR EQUALITIES AND ONQUADRATICS; 6. EXPERIMENTS; 7. CONCLUSION
• Sommario/riassunto: Nonlinear Programming 4