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1、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-x2A2-12;定义目标函数梯度函数 dfun function f=dfun(x) x2=x(2);f=4;-2*x2;定义等式约束函数 hf function qua=hf(x) qua=25-x(1)A2-x(2)A2;定义等式约束函数梯度函数 dhf function qua=dhf(x) qua=-2*x(1);-2*x(2);定义不等式约束函数 gfun function inq=gfun(x) inq=10*x(1)-x(1)A2+10*x(2)-x(2)A2-
2、34;定义不等式约束梯度数 dgf function 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:l psi=psi-he(i)*mu(i); s1=s1+he(i)A2;endpsi=psi+0.5*sigma*s1;s2=0.0;
3、for i=1:ms3=max(0.0, lambda(i) - sigma*gi(i);s2=s2+s3A2-lambda(i)A2;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:ldp
4、si=dpsi+(sigma*he(i)-mu(i)*dhe(:,i);endfor i=1:m dpsi=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;sigma1=0.4;epsilon1=1e-4;k=0;n=length(x0);Bk=eye(n);while(kmaxk) gk=feval(dmpsi,x0,fun,hf,gfun,
5、dfun,dhf,dgf,mu,lambda,sigma); if(norm(gk)epsilon1)break;enddk=-Bkgk;m=0;mk=0; while(m20)newf=feval(mpsi,x0+rhoAm*dk,fun,hf,gfun,dfun,dhf,dgf,mu,lambda,sigma); oldf=feval(mpsi,x0,fun,hf,gfun,dfun,dhf,dgf,mu,lambda,sigma);if(n ewf0)Bk=Bk-(Bk*sk)*sk*Bk)/(sk*Bk*sk)+(yk*yk)/(yk*sk);endk=k+1;x0=x;end val
6、=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,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);gi=feval(gfun,x);l=length(he);m=length(gi);mu=0.1*ones(l,1);lambda=0.1*ones(m,1);btak=10
7、;btaold=10;while(btakepsilon&kepsilonif(k=2&btak theta*btaold) sigma=eta*sigma;endfor i=1:l mu(i)=mu(i)-sigma*he(i);endfor i=1:m lambda(i)=max(0.0,lambda(i)-sigma*gi(i);endendk=k+1;btaold=btak;x0=x;endf=feval(fun,x);xfmulambdak运行求解 x0=0;0x0 =00 multphr(fun,hf,gfun,dfun,dhf,dgf,x0)x =1.001281489564374.89871784708758f =-31.9923105871169mu =1.01559644571312lambda =0.7544511679772284
大连理工优化方法增广拉格朗日方法MATLAB程序
