内容简介

Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds tothe growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practicalproblems.Drawing on their experiences in teaching, research, andconsulting, the authors have produced a textbook that will be of interestto students and practitioners alike. Each chapter begins with the basicconcepts and builds up gradually to the best techniques currentlyavailable.Because of the emphasis on practical methods, as well as theextensive illustrations and exercises, the book is accessible to a wideaudience. It can be used as a graduate text in engineering, operationsresearch, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field.Above all, theauthors have strived to produce a text that is pleasant to read,informative, and rigorous - one that reveals both the beautiful nature ofthe discipline and its practical side.MMOR Mathematical Methods ofOperations Research, 2001: "The book looks very suitable to be used in angraduate-level course in optimization for students in mathematics,operations research, engineering, and others. Moreover, it seems to bevery helpful to do some self-studies in optimization, to complete ownknowledge and can be a source of new ideas.... I recommend this excellentbook to everyone who is interested in optimization problems."

精彩摘录

It(BFGS)isalsomorenumericallystable,andhasveryeffective“self-correctingproperties”notsharedbyDFP,whichmayaccountforitssuperiorperformanceinpractice.

——引自第46页

Inasense,thelinesearchandtrust-regionapproachesdifferintheorderinwhichtheychoosethedirectionanddistanceofthemovetothenextiterate.Linesearchstartsbyfixingthedirectionpkandthenidentifyinganappropriatedistance,namelythesteplengthαk.Intrustregion,wefirstchooseamaximumdistance—thetrust-regionradiusk—andthenseekadirectionandstepthatattainthebestimprovementpossiblesubjecttothisdistanceconstraint.Ifthisstepprovestobeunsatisfactory,wereducethedistancemeasurekandtryagain.

——引自第39页