大连理工优化方法-增广拉格朗日方法MATLAB程序

1、精品文档上机大作业II定义目标函数funfunction f=fun(x)x1=x(1);x2=x(2);f=4*x1-x22-12;定义目标函数梯度函数dfunfunction f=dfun(x)x2=x(2);f=4;-2*x2;定义等式约束函数hffunction qua=hf(x)qua=25-x(1)2-x(2)2;定义等式约束函数梯度函数dhffunction qua=dhf(x)qua=-2*x(1);-2*x(2);定义不等式约束函数gfunfunction inq=gfun(x)inq=10*x(1)-x(1)2+10*x(2)-x(2)2-34;随意编辑精品文档定义不等式约

2、束梯度数dgffunction inq=dgf(x)inq=10-2*x(1);10-2*x(2);定义增广拉格朗日函数mpsifunction psi=mpsi(x,fun,hf,gfun,dfun,dhf,dgf,mu,lambda,sigma)f=feval(fun,x);he=feval(hf,x);gi=feval(gfun,x);l=length(he);m=length(gi);psi=f;s1=0;for i=1:lpsi=psi-he(i)*mu(i);s1=s1+he(i)2;endpsi=psi+0.5*sigma*s1;s2=0.0;for i=1:ms3=max(0.

3、0, lambda(i) - sigma*gi(i);s2=s2+s32-lambda(i)2;随意编辑精品文档endpsi=psi+s2/(2.0*sigma);定义增广拉格朗日函数梯度函数dmpsifunction dpsi=dmpsi(x,fun,hf,gfun,dfun,dhf,dgf,mu,lambda,sigma)dpsi=feval(dfun,x);he=feval(hf,x);gi=feval(gfun,x);dhe=feval(dhf,x);dgi=feval(dgf,x);l=length(he);m=length(gi);for i=1:ldpsi=dpsi+(sigma

4、*he(i)-mu(i)*dhe(:,i);endfor i=1:mdpsi=dpsi+(sigma*gi(i)-lambda(i)*dgi(:,i);end定义 BFGS 法函数函数bfgsfunction x,val,k=bfgs(mpsi,dmpsi,x0,fun,hf,gfun,dfun,dhf,dgf,mu,lambda,sigma)maxk=1000;rho=0.5;随意编辑精品文档sigma1=0.4;epsilon1=1e-4;k=0;n=length(x0);Bk=eye(n);while(k<maxk)gk=feval(dmpsi,x0,fun,hf,gfun,dfu

5、n,dhf,dgf,mu,lambda,sigma);if(norm(gk)<epsilon1)break;enddk=-Bkgk;m=0;mk=0;while(m<20)newf=feval(mpsi,x0+rhom*dk,fun,hf,gfun,dfun,dhf,dgf,mu,lambda,sigma);oldf=feval(mpsi,x0,fun,hf,gfun,dfun,dhf,dgf,mu,lambda,sigma);if(newf<oldf+sigma1*rhom*gk'*dk)mk=m;break;endm=m+1;随意编辑精品文档endx=x0+rho

6、mk*dk;sk=x-x0;yk=feval(dmpsi,x,fun,hf,gfun,dfun,dhf,dgf,mu,lambda,sigma)-gk;if(yk'*sk>0)Bk=Bk-(Bk*sk)*sk'*Bk)/(sk'*Bk*sk)+(yk*yk')/(yk'*sk);endk=k+1;x0=x;endval=feval(mpsi,x0,fun,hf,gfun,dfun,dhf,dgf,mu,lambda,sigma);定义增广拉格朗日乘子法函数multphrfunction answer=multphr(fun,hf,gfun,dfun

7、,dhf,dgf,x0)maxk=5000;sigma=2.0;eta=2.0;theta=0.8;k=0;ink=0;epsilon=1e-4;x=x0;he=feval(hf,x);随意编辑精品文档gi=feval(gfun,x);l=length(he);m=length(gi);mu=0.1*ones(l,1);lambda=0.1*ones(m,1);btak=10;btaold=10;while(btak>epsilon&&k<maxk)x,v,ik=bfgs('mpsi','dmpsi',x0,fun,hf,gfun,dfun,dhf,dgf,mu,lambda,sigma);ink=ink+ik;he=feval(hf,x);gi=feval(gfun,x);btak=0.0;for i=1:lbta