LEADER 00933nam2 22002533i 450 001 LIA0950976 005 20231121125512.0 100 $a20150202d1913 ||||0itac50 ba 101 | $aita$alat 102 $ait 181 1$6z01$ai $bxxxe 182 1$6z01$an 200 0 $a1$fG. B. Gandino 210 $aTorino [etc.]$cParavia e C.$dstampa 1913 215 $aIV, 240 p.$d21 cm. 461 1$1001NAP0081536$12001 $a˜La œsintassi latina$emostrata con luoghi delle opere di Cicerone$ftradotti ed annotati per uso di retroversione ne' ginnasi e ne' licei da G. B. Gandino$v1 801 3$aIT$bIT-01$c20150202 850 $aIT-FR0017 899 $aBiblioteca umanistica Giorgio Aprea$bFR0017 $eN 912 $aLIA0950976 950 2$aBiblioteca umanistica Giorgio Aprea$d 52DFV A 37$e 52BUN0000120965 VMC RF $fB $h20150202$i20150202 977 $a 52 996 $a1$961339 997 $aUNICAS LEADER 05364nam 2200673Ia 450 001 9911020172103321 005 20200520144314.0 010 $a9786613306210 010 $a9781283306218 010 $a1283306212 010 $a9781118032794 010 $a1118032799 010 $a9781118031049 010 $a1118031040 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(Perlego)2771151 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 $epractical optimization and duality /$fWilfred Kaplan 210 $aNew York $cWiley$dc1999 215 $a1 online resource (298 p.) 225 1 $aWiley-Interscience series in discrete mathematics and optimization 300 $a"A Wiley-Interscience publication." 311 08$a9780471252894 311 08$a0471252891 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 $aMathematical optimization 615 0$aMaxima and minima. 615 0$aMathematical optimization. 676 $a511/.66 700 $aKaplan$b Wilfred$f1915-$026105 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911020172103321 996 $aMaxima and minima with applications$94418600 997 $aUNINA