LEADER 05328nam 2200649Ia 450 001 9910139583403321 005 20170809161006.0 010 $a1-283-30621-2 010 $a9786613306210 010 $a1-118-03279-9 010 $a1-118-03104-0 035 $a(CKB)2550000000055758 035 $a(EBL)694832 035 $a(OCoLC)768204518 035 $a(SSID)ssj0000555102 035 $a(PQKBManifestationID)11377666 035 $a(PQKBTitleCode)TC0000555102 035 $a(PQKBWorkID)10517279 035 $a(PQKB)10523803 035 $a(MiAaPQ)EBC694832 035 $a(EXLCZ)992550000000055758 100 $a19980410d1999 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMaxima and minima with applications$b[electronic resource] $epractical optimization and duality /$fWilfred Kaplan 210 $aNew York $cWiley$dc1999 215 $a1 online resource (298 p.) 225 1 $aWiley-Interscience series in discrete mathematics and optimization 300 $a"A Wiley-Interscience publication." 311 $a0-471-25289-1 320 $aIncludes bibliographical references and index. 327 $aMaxima and Minima with Applications: Practical Optimization and Duality; Contents; Preface; 1 Maxima and Minima in Analytic Geometry; 1.1 Maxima and Minima; Case of Functions of One Variable; Problems 1.1-1.5; 1.2 Convexity; 1.3 Convexity and Maxima and Minima; Problems 1.6-1.16; 1.4 Problems in Two Dimensions; Problems 1.17-1.27; 1.5 Some Geometric Extremum Problems; Problems 1.28-1.36; 1.6 Geometry of n-Dimensional Space; 1.7 Convex Functions of n Variables; 1.8 Quadratic Forms; Problems 1.37-1.55; 1.9 Convexity and Extrema, Level Sets and Sublevel Sets; Problems 1.56-1.63; 1.10 Stability 327 $a1.11 Global Asymptotic Stability, Application to Finding MinimizerProblems 1.64-1.73; 1.12 Extrema of Functions on Unbounded Closed Sets; 1.13 Shortest Distance from a Linear Variety; Problems 1.74-1.84; 1.14 Other Inner Products and Norms in Rn; 1.15 More on Minimum Problems for Quadratic Functions; Problems 1.85-1.93; 1.16 Physical Applications; Problems 1.94-1.96; 1.17 Best Approximation by Polynomials; Problems 1.97-1.105; References; 2 Side Conditions; 2.1 Review of Vector Calculus; Problems 2.1-2.13; 2.2 Local Maxima and Minima, Side Conditions; Problems 2.14-2.21 327 $a2.3 Second-Derivative TestProblems 2.22-2.26; 2.4 Gradient Method for Finding Critical Points; Problems 2.27-2.28; 2.5 Applications; Problems 2.29-2.33; 2.6 Karush-Kuhn-Tucker Conditions; Problems 2.34-2.37; 2.7 Sufficient Conditions for the Mathematical Programming Problem; 2.8 Proof of the Karush-Kuhn-Tucker Conditions; Problems 2.38-2.49; References; 3 Optimization; 3.1 Convexity; Problems 3.1-3.17; 3.2 Mathematical Programming, Duality; 3.3 Unconstrained Quadratic Optimization; Problems 3.18-3.28; 3.4 Constrained Quadratic Optimization in Rn 327 $a3.5 QP with Inequality Constraints, QP AlgorithmProblems 3.29-3.38; 3.6 Linear Programming; 3.7 Simplex Algorithm; Problems 3.39-3.55; 3.8 LP with Bounded Variables; Problems 3.56-3.62; 3.9 Convex Functions and Convex Programming; Problems 3.63-3.68; 3.10 The Fermat-Weber Problem and a Dual Problem; Problems 3.69-3.76; 3.11 A Duality Relation in Higher Dimensions; Problems 3.77-3.84; References; 4 Fenchel-Rockafellar Duality Theory; 4.1 Generalized Directional Derivative; Problems 4.1-4.5; 4.2 Local Structure of the Boundary of a Convex Set; Problems 4.6-4.8 327 $a4.3 Supporting Hyperplane, Separating HyperplaneProblems 4.9-4.15; 4.4 New Definition of Convex Function, Epigraph, Hypograph; Problems 4.16-4.17; 4.5 Conjugate of Convex and Concave Functions; Problems 4.18-4.24; 4.6 Fenchel Duality Theorem; Problems 4.25-4.32; 4.7 Rockafellar Duality Theorem; 4.8 Proof of Lemma C; Problems 4.33-4.45; 4.9 Norms, Dual Norms, Minkowski Norms; Problems 4.46-4.61; 4.10 Generalized Fermat-Weber Problem; 4.11 Application to Facility Location; Problems 4.62-4.74; References; Appendix: Linear Algebra; Answers to Selected Problems; Index 330 $aThis new work by Wilfred Kaplan, the distinguished author of influential mathematics and engineering texts, is destined to become a classic. Timely, concise, and content-driven, it provides an intermediate-level treatment of maxima, minima, and optimization. Assuming only a background in calculus and some linear algebra, Professor Kaplan presents topics in order of difficulty. In four short chapters, he describes basic concepts and geometric aspects of maxima and minima, progresses to problems with side conditions, introduces optimization and programming, and concludes with an in-depth discuss 410 0$aWiley-Interscience series in discrete mathematics and optimization. 606 $aMaxima and minima 606 $aMathematical optimization 608 $aElectronic books. 615 0$aMaxima and minima. 615 0$aMathematical optimization. 676 $a511.66 676 $a511/.66 676 $a519.3 700 $aKaplan$b Wilfred$f1915-$026105 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910139583403321 996 $aMaxima and minima with applications$92202085 997 $aUNINA LEADER 01172nas 2200409 c 450 001 996208802103316 005 20171201194005.0 035 $a(CKB)1000000000222919 035 $a(DE-599)ZDB2246688-5 035 $a(OCoLC)645370906 035 $a(DE-101)980821479 035 $a(EXLCZ)991000000000222919 100 $a20060810b18942001 |y | 101 0 $afre 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aRevue olympique$eorgane officiel des movement olympique$fComite? 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