无约束优化算法：单纯形法

单纯形法1.算法原理单纯形法的基本思想是:设x(0),x(1)，…,x(n)是Rn中的n+1个点，构成一个当前的单纯形，xmax,xmin定义如下:f(x)=max{f(x(0)),f(x(1)),...,f(x(n))}maxf(x )=min{f(x(0)),f(x⑴),...,f(x(n))}min记x为这个单纯形除去x外的所有顶点的形心，max1(1(-JIi=0x(i)—xmax/x(n+1)=x+(x—x(n+1)=x+(x—xmax)构成新的单纯形，反复上述过程，直2.函数fminsearch函数语法x=fminsearch(fun,x0)x=fminsearch(fun,x0,options)[x,fval]=fminsearch(...)[x,fval,exitflag]=fminsearch(..)[x,fval,exitflag,output]=fminsearch(..J函数输入：fun：目标函数x0:迭代初始点options:函数参数设置函数输出：x:最优点fval:最优点对应的函数值exitflag:函数停止信息1：函数收敛正常停止0：迭代次数，目标函数计算次数达到最大数-1：算法被输出函数停止output:函数运算信息函数使用目标函数程序BanaFun.mfunctionf=BanaFun(x)(不含导数解析式)f=100*(x(2)-x(1)人2)人2+(1-x(1))A2Nelder-Mead Simplex函数不需要导数信息。算法参数设置：SimplexUnc.moptions=optimset('LargeScale','off','gradobj','off','MaxFunEvals',250,'display','iter')函数调用运算：SimplexUnc.moptions=optimset('LargeScale','off','gradobj','on','MaxFunEvals',250,'display','iter')x=[-1.9,2][x,fval,exitflag,output]=fminsearch(@BanaFun,x,options)计算结果IterationFunc-countminf(x)Procedure01267.6213236.42initialsimplex2567.2672expand3712.2776expand4812.2776reflect51012.2776contractinside6126.76772contractinside7136.76772reflect8156.76772contractinside9176.76772contractoutside10196.62983contractinside11216.55249contractinside12236.46084contractinside13246.46084reflect14266.46084contractinside15286.45544contractoutside16306.42801expand17326.40994expand18346.32449expand19366.28548expand20386.00458expand21396.00458reflect22415.43287expand

23425.43287reflect24444.63434expand25454.63434reflect26474.63434contractinside27494.63434contractoutside28514.31027expand29534.31027contractinside30554.00991expand31564.00991reflect32583.55664expand33593.55664reflect34613.23438reflect35633.23438contractinside36652.9515expand37672.82878reflect38692.56426reflect39712.54453contractoutside40732.43615reflect41752.34358reflect42772.28129reflect43792.21473reflect44812.08627reflect45822.08627reflect46841.86677reflect47861.86677contractinside48881.80424reflect49901.58432expand50911.58432reflect51931.27128expand52941.27128reflect53961.05673reflect54981.05673contractinside551000.816708expand561020.816708contractinside571040.816708contractinside581060.760575reflect591080.601009expand601100.601009contractinside611120.516477reflect621140.516477contractinside631150.516477reflect641170.416316expand651190.416316contractinside661200.416316reflect671220.345716reflect681240.345716contractinside691260.285909expand701280.281068reflect711300.22878reflect721320.22878contractinside731340.203104expand741360.148expand751380.0999997expand761400.0999997contractinside771410.0999997reflect781430.0217142expand791450.0217142contractinside801470.0217142contractinside811480.0217142reflect821500.0217142contractinside831520.0217142contractinside841540.0191193reflect851560.00610404expand861580.00610404contractoutside871600.00261955reflect881610.00261955reflect891630.000256151reflect901650.000256151contractinside911660.000256151reflect921680.000256151contractinside931700.00020711contractinside941720.00010357contractinside951742.09236e-005contractinside961762.09236e-005contractinside971781.80497e-006reflect981801.80497e-006contractinside991821.80497e-006contractinside1001841.80497e-006contractinside1011851.80497e-006reflect1021873.74217e-007contractinside1031893.74217e-007contractinside1041913.26526e-007contractinside1051938.07652e-008contractinside1061951.66554e-008contractinside1071971.66554e-008contractinside1081991.66554e-008contractinside1092015.57089e-009contractoutside1102031.86825e-009contractinside1112051.86825e-009contractoutside1122075.53435e-010contractinside1132085.53435e-010reflect1142104.06855e-010contractinsideOptimizationterminated:thecurrentxsatisfiestheterminationcriteriausingOPTIONS.TolXof1.000000e-004andF(X)satisfiestheco