LEADER 04352nam  22006975  450 
001 9910254076803321
005 20220404185945.0
010   $a3-319-30921-8
024 7 $a10.1007/978-3-319-30921-7
035   $a(CKB)3710000000649214
035   $a(EBL)4512615
035   $a(OCoLC)947837426
035   $a(SSID)ssj0001666027
035   $a(PQKBManifestationID)16455287
035   $a(PQKBTitleCode)TC0001666027
035   $a(PQKBWorkID)15000202
035   $a(PQKB)10019850
035   $a(DE-He213)978-3-319-30921-7
035   $a(MiAaPQ)EBC4512615
035   $a(PPN)193444682
035   $a(EXLCZ)993710000000649214
100   $a20160422d2016      u|         0
101 0 $aeng
135   $aurcn#nnn|||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aNumerical optimization with computational errors /$fby Alexander J. Zaslavski
205   $a1st ed. 2016.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016.
215   $a1 online resource (ix, 304 pages)
225 1 $aSpringer Optimization and Its Applications,$x1931-6828 ;$v108
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-319-30920-X 
320   $aIncludes bibliographical references and index.
327   $a1. Introduction -- 2. Subgradient Projection Algorithm -- 3. The Mirror Descent Algorithm -- 4. Gradient Algorithm with a Smooth Objective Function -- 5. An Extension of the Gradient Algorithm -- 6. Weiszfeld's Method -- 7. The Extragradient Method for Convex Optimization -- 8. A Projected Subgradient Method for Nonsmooth Problems -- 9. Proximal Point Method in Hilbert Spaces -- 10. Proximal Point Methods in Metric Spaces -- 11. Maximal Monotone Operators and the Proximal Point Algorithm -- 12. The Extragradient Method for Solving Variational Inequalities -- 13. A Common Solution of a Family of Variational Inequalities -- 14. Continuous Subgradient Method -- 15. Penalty Methods -- 16. Newton's method -- References -- Index. .
330   $aThis book studies the approximate solutions of optimization problems in the presence of computational errors. A number of results are presented on the convergence behavior of algorithms in a Hilbert space; these algorithms are examined taking into account computational errors. The author illustrates that algorithms generate a good approximate solution, if computational errors are bounded from above by a small positive constant. Known computational errors are examined with the aim of determining an approximate solution. Researchers and students interested in the optimization theory and its applications will find this book instructive and informative. This monograph contains 16 chapters; including a chapters devoted to the subgradient projection algorithm, the mirror descent algorithm, gradient projection algorithm, the Weiszfelds method, constrained convex minimization problems, the convergence of a proximal point method in a Hilbert space, the continuous subgradient method, penalty methods and Newton?s method.
410  0$aSpringer Optimization and Its Applications,$x1931-6828 ;$v108
606   $aCalculus of variations
606   $aNumerical analysis
606   $aOperations research
606   $aManagement science
606   $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016
606   $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050
606   $aOperations Research, Management Science$3https://scigraph.springernature.com/ontologies/product-market-codes/M26024
615  0$aCalculus of variations.
615  0$aNumerical analysis.
615  0$aOperations research.
615  0$aManagement science.
615 14$aCalculus of Variations and Optimal Control; Optimization.
615 24$aNumerical Analysis.
615 24$aOperations Research, Management Science.
676   $a519.3
700   $aZaslavski$b Alexander J$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721713
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910254076803321
996   $aNumerical optimization with computational errors$91523527
997   $aUNINA