LEADER 04987nam 2200625 450 001 9910818715003321 005 20230120014756.0 010 $a1-4832-7246-X 035 $a(CKB)3710000000201038 035 $a(EBL)1888494 035 $a(SSID)ssj0001267143 035 $a(PQKBManifestationID)12484209 035 $a(PQKBTitleCode)TC0001267143 035 $a(PQKBWorkID)11254369 035 $a(PQKB)11537527 035 $a(MiAaPQ)EBC1888494 035 $a(EXLCZ)993710000000201038 100 $a20150110h19701970 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNonlinear programming $eproceedings of a symposium conducted by the Mathematics Research Center, The University of Wisconsin, Madison, May 4-6, 1970 /$fedited by J. B. Rosen, O. L. Mangasarian, K. Ritter 210 1$aNew York, New York ;$aLondon, England :$cAcademic Press, Inc.,$d1970. 210 4$dİ1970 215 $a1 online resource (503 p.) 225 0 $aPublication no. 25 of the Mathematics Research Center, The University of Wisconsin Nonlinear programming 300 $aDescription based upon print version of record. 311 $a1-322-47818-X 311 $a0-12-597050-1 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aFront 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 327 $a3. 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 327 $aChapter 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 327 $a2. 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 327 $a1. 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 327 $a3. Necessary conditions and sufficient conditions 330 $aNonlinear Programming 606 $aNonlinear programming$vCongresses 615 0$aNonlinear programming 676 $a519.7/6 676 $a519.76 702 $aRosen$b J. B$g(Judah Ben),$f1922- 702 $aMangasarian$b Olvi L.$f1934- 702 $aRitter$b K$g(Klaus),$f1936- 712 02$aUniversity of Wisconsin--Madison.$bMathematics Research Center. 712 12$aSymposium on Nonlinear Programming 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910818715003321 996 $aNonlinear programming$9356638 997 $aUNINA