LEADER 05471nam 2200685Ia 450 001 9911019669003321 005 20200520144314.0 010 $a9786613294593 010 $a9781283294591 010 $a1283294591 010 $a9781118032701 010 $a1118032705 010 $a9781118030950 010 $a1118030958 035 $a(CKB)2670000000122271 035 $a(EBL)694688 035 $a(OCoLC)761319792 035 $a(SSID)ssj0000554934 035 $a(PQKBManifestationID)11364361 035 $a(PQKBTitleCode)TC0000554934 035 $a(PQKBWorkID)10518430 035 $a(PQKB)10559350 035 $a(MiAaPQ)EBC694688 035 $a(Perlego)2761945 035 $a(EXLCZ)992670000000122271 100 $a19970408d1997 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aInterior point algorithms $etheory and analysis /$fYinyu Ye 210 $aNew York $cWiley$dc1997 215 $a1 online resource (438 p.) 225 1 $aWiley-Interscience series in discrete mathematics and optimization 300 $aDescription based upon print version of record. 311 08$a9780471174202 311 08$a0471174203 320 $aIncludes bibliographical references (p. 365-408) and index. 327 $aInterior Point Algorithms: Theory and Analysis; Contents; Preface; List of Figures; 1 Introduction and Preliminaries; 1.1 Introduction; 1.2 Mathematical Preliminaries; 1.2.1 Basic notations; 1.2.2 Convex sets; 1.2.3 Real functions; 1.2.4 Inequalities; 1.3 Decision and Optimization Problems; 1.3.1 System of linear equations; 1.3.2 System of nonlinear equations; 1.3.3 Linear least-squares problem; 1.3.4 System of linear inequalities; 1.3.5 Linear programming (LP); 1.3.6 Quadratic programming (QP); 1.3.7 Linear complementarity problem (LCP); 1.3.8 Positive semi-definite programming (PSP) 327 $a1.3.9 Nonlinear programming (NP)1.3.10 Nonlinear complementarity problem (NCP); 1.4 Algorithms and Computation Models; 1.4.1 Worst-case complexity; 1.4.2 Condition-based complexity; 1.4.3 Average complexity; 1.4.4 Asymptotic complexity; 1.5 Basic Computational Procedures; 1.5.1 Gaussian elimination method; 1.5.2 Choleski decomposition method; 1.5.3 The Newton method; 1.5.4 Solving ball-constrained linear problem; 1.5.5 Solving ball-constrained quadratic problem; 1.6 Notes; 1.7 Exercises; 2 Geometry of Convex Inequalities; 2.1 Convex Bodies; 2.1.1 Center of gravity; 2.1.2 Ellipsoids 327 $a2.2 Analytic Center2.2.1 Analytic center; 2.2.2 Dual potential function; 2.2.3 Analytic central-section inequalities; 2.3 Primal and Primal-Dual Potential Functions; 2.3.1 Primal potential function; 2.3.2 Primal-dual potential function; 2.4 Potential Functions for LP, LCP, and PSP; 2.4.1 Primal potential function for LP; 2.4.2 Dual potential function for LP; 2.4.3 Primal-dual potential function for LP; 2.4.4 Potential function for LCP; 2.4.5 Potential function for PSP; 2.5 Central Paths of LP, LCP, and PSP; 2.5.1 Central path for LP; 2.5.2 Central path for LCP; 2.5.3 Central path for PSP 327 $a2.6 Notes2.7 Exercises; 3 Computation of Analytic Center; 3.1 Proximity to Analytic Center; 3.2 Dual Algorithms; 3.2.1 Dual Newton procedure; 3.2.2 Dual potential algorithm; 3.2.3 Central-section algorithm; 3.3 Primal Algorithms; 3.3.1 Primal Newton procedure; 3.3.2 Primal potential algorithm; 3.3.3 Affine scaling algorithm; 3.4 Primal-Dual (Symmetric) Algorithms; 3.4.1 Primal-dual Newton procedure; 3.4.2 Primal-dual potential algorithm; 3.5 Notes; 3.6 Exercises; 4 Linear Programming Algorithms; 4.1 Karmarkar's Algorithm; 4.2 Path-Following Algorithm; 4.3 Potential Reduction Algorithm 327 $a4.4 Primal-Dual (Symmetric) Algorithm4.5 Adaptive Path-Following Algorithms; 4.5.1 Predictor-corrector algorithm; 4.5.2 Wide-neighborhood algorithm; 4.6 Affine Scaling Algorithm; 4.7 Extensions to QP and LCP; 4.8 Notes; 4.9 Exercises; 5 Worst-Case Analysis; 5.1 Arithmetic Operation; 5.2 Termination; 5.2.1 Strict complementarity partition; 5.2.2 Project an interior point onto the optimal face; 5.3 Initialization; 5.3.1 A HSD linear program; 5.3.2 Solving (HSD); 5.3.3 Further analysis; 5.4 Infeasible-Starting Algorithm; 5.5 Notes; 5.6 Exercises; 6 Average-Case Analysis; 6.1 One-Step Analysis 327 $a6.1.1 High-probability behavior 330 $aThe first comprehensive review of the theory and practice of one of today's most powerful optimization techniques.The explosive growth of research into and development of interior point algorithms over the past two decades has significantly improved the complexity of linear programming and yielded some of today's most sophisticated computing techniques. This book offers a comprehensive and thorough treatment of the theory, analysis, and implementation of this powerful computational tool.Interior Point Algorithms provides detailed coverage of all basic and advanced aspects of th 410 0$aWiley-Interscience series in discrete mathematics and optimization. 606 $aProgramming (Mathematics) 606 $aLinear programming 615 0$aProgramming (Mathematics) 615 0$aLinear programming. 676 $a519.7/2 700 $aYe$b Yinyu$0771525 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911019669003321 996 $aInterior point algorithms$94416944 997 $aUNINA LEADER 01577nas 2200505- 450 001 9910895957403321 005 20241126213016.0 035 $a(DE-599)ZDB2625616-2 035 $a(OCoLC)762018781 035 $a(CKB)110978984249198 035 $a(CONSER)--2024242813 035 $a(EXLCZ)99110978984249198 100 $a20110601a19859999 --- - 101 0 $aeng 135 $aurmnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe adult learner 210 1$aDublin :$cAdult Education Organisers' Association,$d1985- 215 $a1 online resource 300 $a"The Irish Journal of Adult and Community Education." 311 08$a0790-8040 531 $aADULT LEARNER 606 $aAdult education$zIreland$vPeriodicals 606 $aCommunity education$zIreland$vPeriodicals 606 $aÉducation des adultes$zIrlande$vPériodiques 606 $aÉducation communautaire$zIrlande$vPériodiques 606 $aCommunity education$2fast 606 $aAdult education$2fast 607 $aIreland$2fast 608 $aPeriodicals.$2fast 608 $aSerial publications.$2lcgft 615 0$aAdult education 615 0$aCommunity education 615 6$aÉducation des adultes 615 6$aÉducation communautaire 615 7$aCommunity education. 615 7$aAdult education. 676 $a374.9417 712 02$aAdult Education Organisers' Association, 906 $aJOURNAL 912 $a9910895957403321 996 $aThe Adult learner$94260770 997 $aUNINA