Title 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

Published Burlington : Academic Press/Elsevier Science, [2014], ©1970

Click on the following:
ProQuest Ebook Central

Copies

Description 1 online resource (503 pages) Series Publication no. 25 of the Mathematics Research Center, The University of Wisconsin Publication ... of the Mathematics Research Center, the University of Wisconsin ; no. 25. Contents 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 the Principle 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 Summary Nonlinear Programming contains the proceedings of a Symposium on Nonlinear Programming held in Madison, Wisconsin on May 4-6, 1970. This book emphasizes algorithms and related theories that lead to efficient computational methods for solving nonlinear programming problems. This compilation consists of 17 chapters. Chapters 1 to 9 are concerned primarily with computational algorithms, while Chapters 10 to 13 are devoted to theoretical aspects of nonlinear programming. Certain applications of nonlinear programming are considered in Chapters 14 to 17. The algorithms for nonlinear constrain Notes 3. Necessary conditions and sufficient conditions Nonlinear Programming Print version record Subject Nonlinear programming -- Congresses MATHEMATICS -- Applied. MATHEMATICS -- Probability & Statistics -- General. Nonlinear programming. Genre/Form Conference papers and proceedings. Form Electronic book Author Rosen, J. B. (Judah Ben), 1922- Mangasarian, Olvi L., 1934- Ritter, K. (Klaus), 1936- University of Wisconsin--Madison. Mathematics Research Center. ISBN 9781483272467 148327246X

  Permalink