000			03488nam a22005055i 4500
001			978-1-4614-4642-2
003			DE-He213
005			20140220083250.0
007			cr nn 008mamaa
008			120810s2012 xxu| s |||| 0|eng d
020			_a9781461446422 _9978-1-4614-4642-2
024	7		_a10.1007/978-1-4614-4642-2 _2doi
050		4	_aQA76.9.A43
072		7	_aPBKS _2bicssc
072		7	_aCOM051300 _2bisacsh
082	0	4	_a518.1 _223
100	1		_aLevy, Adam B. _eauthor.
245	1	0	_aStationarity and Convergence in Reduce-or-Retreat Minimization _h[electronic resource] / _cby Adam B. Levy.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2012.
300			_aXII, 55 p. 3 illus., 1 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		_aSpringerBriefs in Optimization, _x2190-8354
520			_aStationarity and Convergence in Reduce-or-Retreat Minimization presents and analyzes a unifying framework for a wide variety of numerical methods in optimization. The author’s “reduce-or-retreat” framework is a conceptual method-outline that covers any method whose iterations choose between reducing the objective in some way at a trial point, or retreating to a closer set of trial points. The alignment of various derivative-based methods within the same framework encourages the construction of new methods, and inspires new theoretical developments as companions to results from across traditional divides. The text illustrates the former by developing two generalizations of classic derivative-based methods which accommodate non-smooth objectives, and the latter by analyzing these two methods in detail along with a pattern-search method and the famous Nelder-Mead method.In addition to providing a bridge for theory through the “reduce-or-retreat” framework, this monograph extends and broadens the traditional convergence analyses in several ways. Levy develops a generalized notion of approaching stationarity which applies to non-smooth objectives, and explores the roles of the descent and non-degeneracy conditions in establishing this property. The traditional analysis is broadened by considering “situational” convergence of different elements computed at each iteration of a reduce-or-retreat method. The “reduce-or-retreat” framework described in this text covers specialized minimization methods, some general methods for minimization and a direct search method, while providing convergence analysis which complements and expands existing results.
650		0	_aMathematics.
650		0	_aComputer science _xMathematics.
650		0	_aAlgorithms.
650		0	_aMathematical optimization.
650		0	_aDistribution (Probability theory).
650	1	4	_aMathematics.
650	2	4	_aAlgorithms.
650	2	4	_aOptimization.
650	2	4	_aComputational Mathematics and Numerical Analysis.
650	2	4	_aProbability Theory and Stochastic Processes.
650	2	4	_aCalculus of Variations and Optimal Control; Optimization.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461446415
830		0	_aSpringerBriefs in Optimization, _x2190-8354
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-4642-2
912			_aZDB-2-SMA
999			_c101510 _d101510