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1、毕业论文题目无约束优化问题算法初探英文题目UnconstrainedOptimizationAlgorithmisDiscussed院系理学院专业数学与应用数学姓名班级指导教师二零一二年三月摘要对于无约束最优化问题可表述为，（1）其中f(x)是连续可微函数。无约束条件下多变量函数的寻优方法大致分成两类。一类在迭代过程中仅用到函数值,不必计算函数的导数,这类方法称为直接法或搜索法。一般说来,直接法的收敛速度较慢,只是在变量较少时才适用。但迭代法的迭代步骤简单,特别是当目标函数的解析表达式十分复杂,甚至写不出具体表达式时,他们的导数很难求得,或根本不存在，这时,就只有用直
2、接法了。另一类是在计算过程中要用到函数的一阶导数和(或)二阶导数,这时，在(1)中总假定f(x)有一阶或二阶连续偏导数.由于用到函数的解析性质,故称为解析法。【关键词】关键词无约束优化牛顿迭代信赖域算法梯度法AbstractForunconstrainedoptimizationproblemcanbeexpressedas,(1)whichf(x)iscontinuouslydifferentiablefunctions.Noconstraintconditionsofmultivariatefunctionoptimizationmethodroughlydivi
3、dedintotwocategories.Aclassintheiterationprocessonlyusefunctionvalues,neednotcalculationfunctionofderivatives,thiskindofmethodiscalleddirectmethodorsearchmethod.Generallyspeaking,thedirectmethodofconvergencespeedisslow,justinthevariableissmalltoapply.Butiterativemethodofsimpleiterativep
4、rocedure,especiallywhentheanalyticalexpressionoftheobjectivefunctionisverycomplex,andevencouldnotwriteaconcreteexpression,theirderivativeisdifficulttobecalculated,orsimplydidnotexist,then,isonlyinthedirectmethod.Anotherkindisintheprocessofcalculationtouseafunctionofderivativesand(or)sec
5、ondorderderivative,atthismoment,in(1)willalwaysassumethatf(x)haveaoneorderortwoordercontinuouspartialderivative.Becauseoftheusefunctionanalyticpropertiessocalledtheanalyticmethod.[Keywords]Unconstrainedoptimization,Newtoniterative,Trustregionalgorithm，Gradientmethod目录引言.................
6、.............................................1第一章直接法.....................................................2第二章牛顿法及其修正算法.........................................32.1牛顿法..........................................................32.1.1原始牛顿法....................................................
7、42.1.2阻尼牛顿法....................................................62.1.3修正牛顿法....................................................72.2拟牛顿法........................................................82.3牛顿-拉弗森方法.................................................9第三章梯度法（最速下降法）.............
