Matlab優(yōu)化工具箱函數(shù)簡(jiǎn)介(doc 8頁(yè)).doc

1、Matlab優(yōu)化工具箱函數(shù)簡(jiǎn)介一維搜索問題 fminbnd無(wú)約束極小值 fminunc, fminsearch約束極小值 fmincon線性規(guī)劃 linprog二次規(guī)劃 quadprog1 一維搜索問題優(yōu)化工具箱函數(shù) fminbnd對(duì)應(yīng)問題： min f(x) x1x0表示計(jì)算收斂，exitflag=0表示超過了最大的迭代次數(shù)，exitflag0表示計(jì)算不收斂，返回值output有3個(gè)分量，其中iterations是優(yōu)化過程中迭代次數(shù)，funcCount是代入函數(shù)值的次數(shù)，algorithm是優(yōu)化所采用的算法。例：clearfun=(x5+x3+x2-1)/(exp(x2)+sin(-x)ez

2、plot(fun,-2,2)X,fval,exitflag,output= fminbnd(fun,-2,2)結(jié)果為：X = 0.2176fval =-1.1312exitflag = 1output = iterations: 13 funcCount: 13 algorithm: golden section search, parabolic interpolation2 無(wú)約束極小值優(yōu)化工具箱函數(shù) fminunc, fminsearch以上兩個(gè)函數(shù)均可求解無(wú)約束多元函數(shù)的最小值。調(diào)用格式：x=fminunc(fun,X0)x=fminsearch(fun,X0) -以X0為初始迭代點(diǎn)，

3、求使函數(shù)fun取得最小值的xx,fval= fminunc(fun,X0)x,fval= fminsearch(fun,X0)-以X0為初始迭代點(diǎn)，求得最優(yōu)點(diǎn)x和最優(yōu)值fval。fminsearch()采用單純形法進(jìn)行計(jì)算，適合處理階次低但是間斷點(diǎn)多的函數(shù)；fminunc()對(duì)于高階連續(xù)的函數(shù)比較有效,該函數(shù)可以輸出海塞矩陣。例1：求X0=1,1 x,fval=fminunc(3*x(1)2+2*x(1)*x(2)+x(2)2,X0)x,fval=fminsearch(3*x(1)2+2*x(1)*x(2)+x(2)2,1,1)例2：clearfun=exp(x(1)*(2*x(1)2+3*x

4、(2)2+2*x(1)*x(2)+3*x(2)+1);x0=0,0;options=optimset(largescale,off,display,iter,tolx,1e-8,tolfun,1e-8);x,fval,exitflag,output,grad,hessian=fminunc(fun,x0,options)3 約束極小值優(yōu)化工具箱函數(shù) fmincon對(duì)應(yīng)數(shù)學(xué)模型：min F(X) subject to: A*X = B, Aeq*X = Beq (linear constraints) C(X) = 0, Ceq(X) = 0 (nonlinear constraints) LB

5、 = X = UB 調(diào)用格式：x=fmincon(fun,x0,A,b):給定初值x0，求解fun函數(shù)的最極值點(diǎn)x.。約束條件為線性約束A*x0表示優(yōu)化結(jié)果收斂于解，exitflag=0表示優(yōu)化超過了函數(shù)值的計(jì)算次數(shù)，exitflag0表示優(yōu)化不收斂。lambda是拉格朗日乘子，顯示那個(gè)約束條件有效。grad表示梯度，hessian表示漢森矩陣。4 線性規(guī)劃 優(yōu)化函數(shù)linprogX=linprog (f,A,b)對(duì)應(yīng)數(shù)學(xué)規(guī)劃：min f*x subject to: A*x = bX= linprog (f,A,b,Aeq,beq) 增加等式約束Aeq*x = beq.X= linprog (

6、f,A,b,Aeq,beq,LB,UB) 設(shè)計(jì)變量有上下限X= linprog (f,A,b,Aeq,beq,LB,UB,X0) X0為初始迭代點(diǎn)X，F(xiàn)=linprog(.)5 二次規(guī)劃 x= quadprog(H,f,A,b) x = quadprog(H,f,A,b,Aeq,beq) x = quadprog(H,f,A,b,Aeq,beq,lb,ub) x = quadprog(H,f,A,b,Aeq,beq,lb,ub,x0) x = quadprog(H,f,A,b,Aeq,beq,lb,ub,x0,options) x,fval = quadprog(.) x,fval,exitflag = quadprog(.) x,fval,exitflag,output = quadprog(.) x,fval,exitflag,output,lambda = quadprog(.)其中：X=quadprog (H,f,A,b) 對(duì)應(yīng)問題為：min 0.5*x*H*x + f*x subject to: A*x = b X= quadprog (H,f,A,b,Aeq,beq) 增加等式約束Aeq*x = beq.X= quadprog (H,f,A,b,Aeq,beq