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Nonlinear programming : proceedings of a symposium conducted by the Mathematics Research Center, The University of Wisconsin, Madison, May 4-6, 1970 / / edited by J. B. Rosen, O. L. Mangasarian, K. Ritter
| Nonlinear programming : proceedings of a symposium conducted by the Mathematics Research Center, The University of Wisconsin, Madison, May 4-6, 1970 / / edited by J. B. Rosen, O. L. Mangasarian, K. Ritter |
| Pubbl/distr/stampa | New York, New York ; ; London, England : , : Academic Press, Inc., , 1970 |
| Descrizione fisica | 1 online resource (503 p.) |
| Disciplina |
519.7/6
519.76 |
| Collana | Publication no. 25 of the Mathematics Research Center, The University of Wisconsin Nonlinear programming |
| Soggetto topico | Nonlinear programming |
| ISBN | 1-4832-7246-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; Nonlinear Programming; Copyright Page; Table of Contents; Foreword; Preface; Chapter 1. A Method of Centers by Upper-Bounding Functions with Applications; ABSTRACT; Introduction; 1. The Method of Centers: A Summary with Modifications; 2. Method of Centers (General algorithm; 3. Method of Center by Upper-Bounding Functions; 4. Applications of the Method of Centers by Upper- BoundingFunctions; REFERENCES; Chapter 2. A New Algorithm for Unconstrained Optimization; ABSTRACT; 1. Introduction; 2. The Formula for Revising the Second DerivativeApproximation
3. An Outline of the New Algorithm4. Theorems on the New Algorithm; Acknowledgements; REFERENCES; Chapter 3. A Class of Methods for Nonlinear ProgrammingII Computational Experience; ABSTRACT; Introduction; 2. A Basic Approach; 3. Algorithms based on Variable Metric methods; 4. Inequality Constraints; REFERENCES; Chapter 4. Some Algorithms Based on thePrinciple of Feasible Directions; ABSTRACT; 1. Introduction; 2. Direction generators; 3. Unconstrained Optimization; 4. Linearly Constrained Nonlinear Programming; 5. A partitioning method; REFERENCES Chapter 5. Numerical Techniques in Mathematical ProgrammingABSTRACT; Introduction; A. THE USE OF LU DECOMPOSITION INEXCHANGE ALGORITHMS; B. THE QR DECOMPOSITION ANDQUADRATIC PROGRAMMING; C. THE SVD AND NONLINEAR LEASTSQUARES; REFERENCES; Chapter 6. A Superlinearly Convergent Method forUnconstrained Minimization; ABSTRACT; 1. Introduction; 2. Formulation of the problem, definitions and notation; 3. The algorithm; 4. Special convergence properties of the algorithm; REFERENCES; Chapter 7. A Second Order Method for the Linearly ConstrainedNonlinear Programming Problem; ABSTRACT; 1. Introduction 2. The algorithm3. Convergence of the Algorithm; 4. Rate of Convergence of the Algorithm; 5. Discussion; REFERENCES; Chapter 8. Convergent Step-Sizes for Gradient-Like FeasibleDirection Algorithms for Constrained Optimization; ABSTRACT; 1. Introduction; 2. Gradient-like feasible direction algorithms; 3. General stepsize criteria; 4. Step sizes based on minimization; 5. Step sizes based on a range function; 6. Step sizes based on a search procedure; 7 Example of directions: variable metric gradientprojections; REFERENCES; Chapter 9. On the Implementation of Conceptual Algorithms; ABSTRACT 1. Introduction2. Conceptual algorithms; 3. Adaptive Procedures for Implementation; 4. Open Loop Procedures for Implementation; 5. Conclusion; REFERENCES; Chapter 10. Some Convex Programs Whose DualsAre Linearly Constrained; ABSTRACT; 1. Introduction; 2. Dual problems; 3. The nature of problem(D1); 4. Examples; 5. Relationships between (P), (D )and (DI); REFERENCES; Chapter 11. Sufficiency Conditions and a Duality Theoryfor Mathematical Programming Problems in Arbitrary Linear Spaces; ABSTRACT; 1. Introduction; 2. Mathematical preliminaries and problem statement 3. Necessary conditions and sufficient conditions |
| Record Nr. | UNINA-9910786631803321 |
| New York, New York ; ; London, England : , : Academic Press, Inc., , 1970 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nonlinear programming : proceedings of a symposium conducted by the Mathematics Research Center, The University of Wisconsin, Madison, May 4-6, 1970 / / edited by J. B. Rosen, O. L. Mangasarian, K. Ritter
| Nonlinear programming : proceedings of a symposium conducted by the Mathematics Research Center, The University of Wisconsin, Madison, May 4-6, 1970 / / edited by J. B. Rosen, O. L. Mangasarian, K. Ritter |
| Pubbl/distr/stampa | New York, New York ; ; London, England : , : Academic Press, Inc., , 1970 |
| Descrizione fisica | 1 online resource (503 p.) |
| Disciplina |
519.7/6
519.76 |
| Collana | Publication no. 25 of the Mathematics Research Center, The University of Wisconsin Nonlinear programming |
| Soggetto topico | Nonlinear programming |
| ISBN | 1-4832-7246-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Front Cover; Nonlinear Programming; Copyright Page; Table of Contents; Foreword; Preface; Chapter 1. A Method of Centers by Upper-Bounding Functions with Applications; ABSTRACT; Introduction; 1. The Method of Centers: A Summary with Modifications; 2. Method of Centers (General algorithm; 3. Method of Center by Upper-Bounding Functions; 4. Applications of the Method of Centers by Upper- BoundingFunctions; REFERENCES; Chapter 2. A New Algorithm for Unconstrained Optimization; ABSTRACT; 1. Introduction; 2. The Formula for Revising the Second DerivativeApproximation
3. An Outline of the New Algorithm4. Theorems on the New Algorithm; Acknowledgements; REFERENCES; Chapter 3. A Class of Methods for Nonlinear ProgrammingII Computational Experience; ABSTRACT; Introduction; 2. A Basic Approach; 3. Algorithms based on Variable Metric methods; 4. Inequality Constraints; REFERENCES; Chapter 4. Some Algorithms Based on thePrinciple of Feasible Directions; ABSTRACT; 1. Introduction; 2. Direction generators; 3. Unconstrained Optimization; 4. Linearly Constrained Nonlinear Programming; 5. A partitioning method; REFERENCES Chapter 5. Numerical Techniques in Mathematical ProgrammingABSTRACT; Introduction; A. THE USE OF LU DECOMPOSITION INEXCHANGE ALGORITHMS; B. THE QR DECOMPOSITION ANDQUADRATIC PROGRAMMING; C. THE SVD AND NONLINEAR LEASTSQUARES; REFERENCES; Chapter 6. A Superlinearly Convergent Method forUnconstrained Minimization; ABSTRACT; 1. Introduction; 2. Formulation of the problem, definitions and notation; 3. The algorithm; 4. Special convergence properties of the algorithm; REFERENCES; Chapter 7. A Second Order Method for the Linearly ConstrainedNonlinear Programming Problem; ABSTRACT; 1. Introduction 2. The algorithm3. Convergence of the Algorithm; 4. Rate of Convergence of the Algorithm; 5. Discussion; REFERENCES; Chapter 8. Convergent Step-Sizes for Gradient-Like FeasibleDirection Algorithms for Constrained Optimization; ABSTRACT; 1. Introduction; 2. Gradient-like feasible direction algorithms; 3. General stepsize criteria; 4. Step sizes based on minimization; 5. Step sizes based on a range function; 6. Step sizes based on a search procedure; 7 Example of directions: variable metric gradientprojections; REFERENCES; Chapter 9. On the Implementation of Conceptual Algorithms; ABSTRACT 1. Introduction2. Conceptual algorithms; 3. Adaptive Procedures for Implementation; 4. Open Loop Procedures for Implementation; 5. Conclusion; REFERENCES; Chapter 10. Some Convex Programs Whose DualsAre Linearly Constrained; ABSTRACT; 1. Introduction; 2. Dual problems; 3. The nature of problem(D1); 4. Examples; 5. Relationships between (P), (D )and (DI); REFERENCES; Chapter 11. Sufficiency Conditions and a Duality Theoryfor Mathematical Programming Problems in Arbitrary Linear Spaces; ABSTRACT; 1. Introduction; 2. Mathematical preliminaries and problem statement 3. Necessary conditions and sufficient conditions |
| Record Nr. | UNINA-9910818715003321 |
| New York, New York ; ; London, England : , : Academic Press, Inc., , 1970 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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
| 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 |
| Pubbl/distr/stampa | New York, New York ; ; London, [England] : , : Academic Press, , 1981 |
| Descrizione fisica | 1 online resource (560 p.) |
| Disciplina | 519.7/6 |
| Soggetto topico | Nonlinear programming |
| ISBN | 1-4832-6017-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910786639203321 |
| New York, New York ; ; London, [England] : , : Academic Press, , 1981 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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
| 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 |
| Pubbl/distr/stampa | New York, New York ; ; London, [England] : , : Academic Press, , 1981 |
| Descrizione fisica | 1 online resource (560 p.) |
| Disciplina | 519.7/6 |
| Soggetto topico | Nonlinear programming |
| ISBN | 1-4832-6017-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910806167603321 |
| New York, New York ; ; London, [England] : , : Academic Press, , 1981 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||