000 03508nam a22005055i 4500
001 978-1-4614-5838-8
003 DE-He213
005 20140220082822.0
007 cr nn 008mamaa
008 130321s2013 xxu| s |||| 0|eng d
020 _a9781461458388
_9978-1-4614-5838-8
024 7 _a10.1007/978-1-4614-5838-8
_2doi
050 4 _aQA276-280
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.5
_223
100 1 _aLange, Kenneth.
_eauthor.
245 1 0 _aOptimization
_h[electronic resource] /
_cby Kenneth Lange.
250 _a2nd ed. 2013.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXVII, 529 p. 19 illus., 3 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Texts in Statistics,
_x1431-875X ;
_v95
505 0 _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.
520 _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.
650 0 _aStatistics.
650 0 _aMathematical optimization.
650 0 _aMathematical statistics.
650 0 _aOperations research.
650 1 4 _aStatistics.
650 2 4 _aStatistical Theory and Methods.
650 2 4 _aOptimization.
650 2 4 _aOperation Research/Decision Theory.
650 2 4 _aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461458371
830 0 _aSpringer Texts in Statistics,
_x1431-875X ;
_v95
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-5838-8
912 _aZDB-2-SMA
999 _c95515
_d95515