LEADER 04334nam 22006374a 450 001 9910451674103321 005 20200520144314.0 010 $a981-277-709-1 035 $a(CKB)1000000000480124 035 $a(StDuBDS)AH24684702 035 $a(SSID)ssj0000130314 035 $a(PQKBManifestationID)11159703 035 $a(PQKBTitleCode)TC0000130314 035 $a(PQKBWorkID)10082019 035 $a(PQKB)11204529 035 $a(MiAaPQ)EBC1681537 035 $a(WSP)00005021 035 $a(PPN)181360314 035 $a(Au-PeEL)EBL1681537 035 $a(CaPaEBR)ebr10201309 035 $a(CaONFJC)MIL491695 035 $a(OCoLC)843333133 035 $a(EXLCZ)991000000000480124 100 $a20020530d2002 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aConvex analysis in general vector spaces$b[electronic resource] /$fC Za?linescu 210 $aRiver Edge, N.J. ;$aLondon $cWorld Scientific$dc2002 215 $a1 online resource (xx, 367 p. ) 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a981-238-067-1 320 $aIncludes bibliographical references (p. 349-357) and index. 327 $ach. 1. Preliminary results on functional analysis. 1.1. Preliminary notions and results. 1.2. Closedness and interiority notions. 1.3. Open mapping theorems. 1.4. Variational principles. 1.5. Exercises. 1.6. Bibliographical notes -- ch. 2. Convex analysis in locally convex spaces. 2.1. Convex functions. 2.2. Semi-continuity of convex functions. 2.3. Conjugate functions. 2.4. The subdifferential of a convex function. 2.5. The general problem of convex programming. 2.6. Perturbed problems. 2.7. The fundamental duality formula. 2.8. Formulas for conjugates and e-subdifferentials, duality relations and optimality conditions. 2.9. Convex optimization with constraints. 2.10. A minimax theorem. 2.11. Exercises. 2.12. Bibliographical notes -- ch. 3. Some results and applications of convex analysis in normed spaces. 3.1. Further fundamental results in convex analysis. 3.2. Convexity and monotonicity of subdifferentials. 3.3. Some classes of functions of a real variable and differentiability of convex functions. 3.4. Well conditioned functions. 3.5. Uniformly convex and uniformly smooth convex functions. 3.6. Uniformly convex and uniformly smooth convex functions on bounded sets. 3.7. Applications to the geometry of normed spaces. 3.8. Applications to the best approximation problem. 3.9. Characterizations of convexity in terms of smoothness. 3.10. Weak sharp minima, well-behaved functions and global error bounds for convex inequalities. 3.11. Monotone multifunctions. 3.12. Exercises. 3.13. Bibliographical notes. 330 $aThis text seeks to present the conjugate and sub/differential calculus using the method of perturbation functions in order to obtain the most general results in this field. Its secondary aim is to provide important applications of this calculus and of the properties of convex functions. 330 $bThe primary aim of this text is to present the conjugate and sub/differential calculus using the method of perturbation functions in order to obtain the most general results in this field. The secondary aim is to provide important applications of this calculus and of the properties of convex functions. Such applications are: the study of well-conditioned convex functions; uniformly convex and uniformly smooth convex functions; best approximation problems; characterizations of convexity; the study of the sets of weak sharp minima; well-behaved functions and the existence of global error bounds for convex inequalities; and the study of monotone multifunctions by using convex functions. 606 $aConvex functions 606 $aConvex sets 606 $aFunctional analysis 606 $aVector spaces 608 $aElectronic books. 615 0$aConvex functions. 615 0$aConvex sets. 615 0$aFunctional analysis. 615 0$aVector spaces. 676 $a515/.8 700 $aZalinescu$b C.$f1952-$0486857 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910451674103321 996 $aConvex analysis in general vector spaces$9282077 997 $aUNINA