LEADER 04539nam 2200757 a 450 001 9910789997403321 005 20230725031355.0 010 $a1-283-16634-8 010 $a9786613166340 010 $a3-11-025021-7 024 7 $a10.1515/9783110250213 035 $a(CKB)2670000000088767 035 $a(EBL)690643 035 $a(OCoLC)723945523 035 $a(SSID)ssj0000530390 035 $a(PQKBManifestationID)11338674 035 $a(PQKBTitleCode)TC0000530390 035 $a(PQKBWorkID)10561275 035 $a(PQKB)10276954 035 $a(MiAaPQ)EBC690643 035 $a(DE-B1597)114002 035 $a(OCoLC)754713662 035 $a(OCoLC)840446286 035 $a(DE-B1597)9783110250213 035 $a(Au-PeEL)EBL690643 035 $a(CaPaEBR)ebr10486547 035 $a(CaONFJC)MIL316634 035 $a(EXLCZ)992670000000088767 100 $a20100910d2011 uy 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aOptimization in function spaces$b[electronic resource] $ewith stability considerations in Orlicz spaces /$fPeter Kosmol, Dieter Mu?ller-Wichards 210 $aBerlin ;$aNew York $cDe Gruyter$d2011 215 $a1 online resource (404 p.) 225 1 $aDe Gruyter series in nonlinear analysis and applications,$x0941-813X ;$v13 300 $aDescription based upon print version of record. 311 0 $a3-11-025020-9 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tPreface --$tContents --$t1 Approximation in Orlicz Spaces --$t2 Polya Algorithms in Orlicz Spaces --$t3 Convex Sets and Convex Functions --$t4 Numerical Treatment of Non-linear Equations and Optimization Problems --$t5 Stability and Two-stage Optimization Problems --$t6 Orlicz Spaces --$t7 Orlicz Norm and Duality --$t8 Differentiability and Convexity in Orlicz Spaces --$t9 Variational Calculus --$tBibliography --$tList of Symbols --$tIndex 330 $aThis is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces. Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equations are developed in this text. A synopsis of the geometry of Banach spaces, aspects of stability and the duality of different levels of differentiability and convexity is developed. A particular emphasis is placed on the geometrical aspects of strong solvability of a convex optimization problem: it turns out that this property is equivalent to local uniform convexity of the corresponding convex function. This treatise also provides a novel approach to the fundamental theorems of Variational Calculus based on the principle of pointwise minimization of the Lagrangian on the one hand and convexification by quadratic supplements using the classical Legendre-Ricatti equation on the other. The reader should be familiar with the concepts of mathematical analysis and linear algebra. Some awareness of the principles of measure theory will turn out to be helpful. The book is suitable for students of the second half of undergraduate studies, and it provides a rich set of material for a master course on linear and nonlinear functional analysis. Additionally it offers novel aspects at the advanced level. From the contents: Approximation and Polya Algorithms in Orlicz Spaces Convex Sets and Convex Functions Numerical Treatment of Non-linear Equations and Optimization Problems Stability and Two-stage Optimization Problems Orlicz Spaces, Orlicz Norm and Duality Differentiability and Convexity in Orlicz Spaces Variational Calculus 410 0$aDe Gruyter series in nonlinear analysis and applications ;$v13. 606 $aStability$xMathematical models 606 $aMathematical optimization 606 $aOrlicz spaces 610 $aBanach space. 610 $aFunctional Analysis. 610 $aOptimization. 610 $aOrlicz space. 610 $aStability. 615 0$aStability$xMathematical models. 615 0$aMathematical optimization. 615 0$aOrlicz spaces. 676 $a515/.392 686 $aSK 600$qSEPA$2rvk 700 $aKosmol$b Peter$01470237 701 $aMu?ller-Wichards$b D$g(Dieter),$f1946-$01470238 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910789997403321 996 $aOptimization in function spaces$93681925 997 $aUNINA