Numerical Nonlinear Optimization

《Numerical Nonlinear Optimization》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、NUMERICALNONLINEAROPTIMIZATIONPhilipE.Gill1andMargaretH.Wright2c2002{2006.AllRightsReserved.1DepartmentofMathematics,UniversityofCalifornia,SanDiego,LaJolla,CA92093,USA.2ComputerScienceDepartment,CourantInstituteofMathematicalSciences,NewYorkUni-versity,NewYork,NY10012,USA.Contents1Intro

2、duction11.1.Introduction...................................12UnconstrainedOptimization52.1.Motivation....................................52.2.Terminology...................................72.3.OptimalityConditions..............................112.4.PropertiesofQuadraticFunctions.........

3、..............172.5.OverviewofMethodsforUnconstrainedOptimization............232.5.1.Formulatingalocallinearmodel....................242.5.2.Formulatingalocalquadraticmodel..................242.5.3.Expressionsforfunctionmodels....................252.5.4.Modelsinline-searchandtrust-region

4、methods............252.6.TheMethodofSteepest-Descent........................262.6.1.Aline-searchsteepest-descentmethod.................272.6.2.Atrust-regionsteepest-descentmethod................302.6.3.Numericalbehaviorofclassicalsteepestdescent...........312.7.Newton'sMethod............

5、....................322.8.ModiedNewtonmethods...........................372.8.1.Steepestdescentinarbitrarynorms..................372.8.2.Newton'smethodassteepestdescent.................372.8.3.Thespectraldecomposition.......................392.8.4.InterpretationofthemodiedNewtondirect

6、ion...........412.9.ChoosingtheLine-SearchStepLength.....................432.9.1.Introduction...............................442.9.2.Theroleofthesteplengthinprovingconvergence..........442.9.3.TheArmijosucientdecreasecondition................452.9.4.Thebacktrackinglinesearch.............

7、.........462.9.5.TheWolfeconditions..........................472.10.Trust-RegionMethods..............................542.10.1.Choosingthetrust-regionnorm....................562.10.2.Approximatesolutionofthetrust-regionsubproblem........572.10.3.Thetwo-normtrust-regionsubp