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Record Nr. |
UNINA9910818715003321 |
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Titolo |
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 |
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Pubbl/distr/stampa |
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New York, New York ; ; London, England : , : Academic Press, Inc., , 1970 |
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©1970 |
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ISBN |
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Descrizione fisica |
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1 online resource (503 p.) |
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Collana |
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Publication no. 25 of the Mathematics Research Center, The University of Wisconsin Nonlinear programming |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references at the end of each chapters and index. |
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Nota di contenuto |
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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 |
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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 |
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Sommario/riassunto |
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