04159nam 22007575 450 991043786440332120250410125610.01-4614-5838-210.1007/978-1-4614-5838-8(CKB)2670000000340830(EBL)1082014(SSID)ssj0000879423(PQKBManifestationID)11477738(PQKBTitleCode)TC0000879423(PQKBWorkID)10868227(PQKB)10331126(DE-He213)978-1-4614-5838-8(MiAaPQ)EBC6311841(MiAaPQ)EBC1082014(Au-PeEL)EBL1082014(CaPaEBR)ebr10983278(OCoLC)831412354(PPN)169135837(EXLCZ)99267000000034083020130321d2013 u| 0engur|n|---|||||txtccrOptimization /by Kenneth Lange2nd ed. 2013.New York, NY :Springer New York :Imprint: Springer,2013.1 online resource (540 p.)Springer Texts in Statistics,2197-4136 ;95Description based upon print version of record.1-4899-9270-7 1-4614-5837-4 Elementary 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.Finite-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.Springer Texts in Statistics,2197-4136 ;95StatisticsMathematical optimizationOperations researchStatisticsStatistical Theory and MethodsOptimizationOperations Research and Decision TheoryStatistics in Engineering, Physics, Computer Science, Chemistry and Earth SciencesStatistics.Mathematical optimization.Operations research.Statistics.Statistical Theory and Methods.Optimization.Operations Research and Decision Theory.Statistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences.519.3Lange Kennethauthttp://id.loc.gov/vocabulary/relators/aut59343MiAaPQMiAaPQMiAaPQBOOK9910437864403321Optimization748060UNINA