LEADER 04159nam 22007575 450 001 9910437864403321 005 20250410125610.0 010 $a1-4614-5838-2 024 7 $a10.1007/978-1-4614-5838-8 035 $a(CKB)2670000000340830 035 $a(EBL)1082014 035 $a(SSID)ssj0000879423 035 $a(PQKBManifestationID)11477738 035 $a(PQKBTitleCode)TC0000879423 035 $a(PQKBWorkID)10868227 035 $a(PQKB)10331126 035 $a(DE-He213)978-1-4614-5838-8 035 $a(MiAaPQ)EBC6311841 035 $a(MiAaPQ)EBC1082014 035 $a(Au-PeEL)EBL1082014 035 $a(CaPaEBR)ebr10983278 035 $a(OCoLC)831412354 035 $a(PPN)169135837 035 $a(EXLCZ)992670000000340830 100 $a20130321d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aOptimization /$fby Kenneth Lange 205 $a2nd ed. 2013. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2013. 215 $a1 online resource (540 p.) 225 1 $aSpringer Texts in Statistics,$x2197-4136 ;$v95 300 $aDescription based upon print version of record. 311 08$a1-4899-9270-7 311 08$a1-4614-5837-4 327 $aElementary Optimization -- The Seven C?s of Analysis -- The Gauge Integral -- Differentiation -- Karush-Kuhn-Tucker Theory -- Convexity -- Block Relaxation -- The MM Algorithm -- The EM Algorithm -- Newton?s Method and Scoring -- Conjugate Gradient and Quasi-Newton -- Analysis of Convergence -- Penalty and Barrier Methods -- Convex Calculus -- Feasibility and Duality -- Convex Minimization Algorithms -- The Calculus of Variations -- Appendix: Mathematical Notes -- References -- Index. 330 $aFinite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theory and development of numerical algorithms. Building on students? skills in calculus and linear algebra, the text provides a rigorous exposition without undue abstraction. Its stress on statistical applications will be especially appealing to graduate students of statistics and biostatistics. The intended audience also includes students in applied mathematics, computational biology, computer science, economics, and physics who want to see rigorous mathematics combined with real applications.   In this second edition, the emphasis remains on finite-dimensional optimization. New material has been added on the MM algorithm, block descent and ascent, and the calculus of variations. Convex calculus is now treated in much greater depth.  Advanced topics such as the Fenchel conjugate, subdifferentials, duality, feasibility, alternating projections, projected gradient methods, exact penalty methods, and Bregman iteration will equip students with the essentials for understanding modern data mining techniques in high dimensions. 410 0$aSpringer Texts in Statistics,$x2197-4136 ;$v95 606 $aStatistics 606 $aMathematical optimization 606 $aOperations research 606 $aStatistics 606 $aStatistical Theory and Methods 606 $aOptimization 606 $aOperations Research and Decision Theory 606 $aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences 615 0$aStatistics. 615 0$aMathematical optimization. 615 0$aOperations research. 615 0$aStatistics. 615 14$aStatistical Theory and Methods. 615 24$aOptimization. 615 24$aOperations Research and Decision Theory. 615 24$aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences. 676 $a519.3 700 $aLange$b Kenneth$4aut$4http://id.loc.gov/vocabulary/relators/aut$059343 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910437864403321 996 $aOptimization$9748060 997 $aUNINA