LEADER 04092nam 2200685Ia 450 001 9911019207003321 005 20200520144314.0 010 $a9786610367009 010 $a9781280367007 010 $a1280367008 010 $a9780470311820 010 $a0470311827 010 $a9780471461661 010 $a0471461660 010 $a9780471249702 010 $a047124970X 035 $a(CKB)111087027121356 035 $a(EBL)157071 035 $a(OCoLC)475872690 035 $a(SSID)ssj0000130321 035 $a(PQKBManifestationID)11146398 035 $a(PQKBTitleCode)TC0000130321 035 $a(PQKBWorkID)10082121 035 $a(PQKB)11452153 035 $a(MiAaPQ)EBC157071 035 $a(PPN)169570053 035 $a(Perlego)2756329 035 $a(EXLCZ)99111087027121356 100 $a20010706d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aConvexity and optimization in R [superscript n] /$fLeonard D. Berkovitz 210 $aNew York $cJ. Wiley$dc2002 215 $a1 online resource (283 p.) 225 1 $aPure and applied mathematicss 300 $aDescription based upon print version of record. 311 08$a9780471352815 311 08$a0471352810 320 $aIncludes bibliographical references (p. 261-262) and index. 327 $aCONVEXITY AND OPTIMIZATION IN R(n); CONTENTS; Preface; I Topics in Real Analysis; 1. Introduction; 2. Vectors in R(n); 3. Algebra of Sets; 4. Metric Topology of R(n); 5. Limits and Continuity; 6. Basic Property of Real Numbers; 7. Compactness; 8. Equivalent Norms and Cartesian Products; 9. Fundamental Existence Theorem; 10. Linear Transformations; 11. Differentiation in R(n); II Convex Sets in R(n); 1. Lines and Hyperplanes in R(n); 2. Properties of Convex Sets; 3. Separation Theorems; 4. Supporting Hyperplanes: Extreme Points; 5. Systems of Linear Inequalities: Theorems of the Alternative 327 $a6. Affine Geometry7. More on Separation and Support; III Convex Functions; 1. Definition and Elementary Properties; 2. Subgradients; 3. Differentiable Convex Functions; 4. Alternative Theorems for Convex Functions; 5. Application to Game Theory; IV Optimization Problems; 1. Introduction; 2. Differentiable Unconstrained Problems; 3. Optimization of Convex Functions; 4. Linear Programming Problems; 5. First-Order Conditions for Differentiable Nonlinear Programming Problems; 6. Second-Order Conditions; V Convex Programming and Duality; 1. Problem Statement 327 $a2. Necessary Conditions and Sufficient Conditions3. Perturbation Theory; 4. Lagrangian Duality; 5. Geometric Interpretation; 6. Quadratic Programming; 7. Duality in Linear Programming; VI Simplex Method; 1. Introduction; 2. Extreme Points of Feasible Set; 3. Preliminaries to Simplex Method; 4. Phase II of Simplex Method; 5. Termination and Cycling; 6. Phase I of Simplex Method; 7. Revised Simplex Method; Bibliography; Index 330 $aA comprehensive introduction to convexity and optimization in RnThis book presents the mathematics of finite dimensional constrained optimization problems. It provides a basis for the further mathematical study of convexity, of more general optimization problems, and of numerical algorithms for the solution of finite dimensional optimization problems. For readers who do not have the requisite background in real analysis, the author provides a chapter covering this material. The text features abundant exercises and problems designed to lead the reader to a fundamental understanding of t 410 0$aPure and applied mathematics (John Wiley & Sons : Unnumbered) 606 $aConvex sets 606 $aMathematical optimization 615 0$aConvex sets. 615 0$aMathematical optimization. 676 $a516/.08 700 $aBerkovitz$b Leonard David$f1924-$0283994 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911019207003321 996 $aConvexity and optimization in R$94419339 997 $aUNINA LEADER 02221oas 2200661 a 450 001 9910229795603321 005 20251202213019.0 035 $a(OCoLC)181028433 035 $a(CONSER) 2010250876 035 $a(CKB)111093463276020 035 $a(EXLCZ)99111093463276020 100 $a20071109b19972002 sy 101 0 $aeng 135 $aurbn||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAustralian mining & petroleum law journal /$fAustralian Mining and Petroleum Law Association Limited in association with the Centre for Commercial and Resources Law of the University of Western Australia and the Centre for Energy and Resources Law of the University of Melbourne 210 $a[Melbourne, Vic.] $c[Australian Mining & Petroleum Law Association] 215 $a1 online resource 311 08$a1328-6803 517 1 $aAustralian Mining & Petroleum L.J. 517 3 $aAustralian mining and petroleum law journal 517 1 $aAMPLAJ 606 $aMining law$zAustralia$vPeriodicals 606 $aPetroleum law and legislation$zAustralia$vPeriodicals 606 $aMining law$2fast$3(OCoLC)fst01022931 606 $aPetroleum law and legislation$2fast$3(OCoLC)fst01059663 607 $aAustralia$2fast$1https://id.oclc.org/worldcat/entity/E39QbtfRv8PPH7gCqhkJ8DK8bM 608 $aPeriodicals.$2fast 615 0$aMining law 615 0$aPetroleum law and legislation 615 7$aMining law. 615 7$aPetroleum law and legislation. 676 $a343.94077005 712 02$aAustralian Mining and Petroleum Law Association 712 02$aCentre for Commercial and Resources Law 712 02$aUniversity of Melbourne.$bCentre for Energy and Resources Law. 801 0$bCLL 801 1$bCLL 801 2$bCLL 801 2$bOCLCQ 801 2$bAU@ 801 2$bNCCHA 801 2$bBUF 801 2$bOCLCQ 801 2$bOCLCF 801 2$bOCLCQ 801 2$bVT2 801 2$bUUM 801 2$bOCLCQ 801 2$bOCLCL 801 2$bOCLCQ 801 2$bU3W 906 $aJOURNAL 912 $a9910229795603321 996 $aAustralian mining & petroleum law journal$92079491 997 $aUNINA