大连理工优化方法-增广拉格朗日方法MATLAB程序.doc

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;定义不等式约束梯度数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:l psi=psi-he(i)*mu(i); s1=s1+he(i)2;endpsi=psi+0.5*sigma*s1;s2=0.0;for i=1:m s3=max(0.0, lambda(i) - sigma*gi(i); s2=s2+s32-lambda(i)2;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:l dpsi=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,dfun,dhf,dgf,mu,lambda,sigma); if(norm(gk)epsilon1) break; end dk=-Bkgk; m=0; mk=0; while(m20) 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(newfoldf+sigma1*rhom*gk*dk) mk=m; break; end m=m+1; end x=x0+rhomk*dk; sk=x-x0; yk=feval(dmpsi,x,fun,hf,gfun,dfun,dhf,dgf,mu,lambda,sigma)-gk; if(yk*sk0) Bk=Bk-(Bk*sk)*sk*Bk)/(sk*Bk*sk)+(yk*yk)/(yk*sk); end k=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,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;btaold=10;while(btakepsilonkmaxk) 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:l btak=btak+he(i)2; end for i=1:m temp=min(gi(i),lambda(i)/sigma); btak=btak+temp2; end btak=sqrt(btak); if btakepsilon if(k=2btak theta*btaold) sigma=eta*sigma; end for i=1:l mu(i)=mu(i)-sigma*he(i); end for i=1:m lambda(i)=max(0.0,lambda(i)-sigma*gi(i); end end k=k+1; btaold=btak; x0=x;endf=feval(fun,x);xfmulambdak运行求解 x0=0;0x0 = 0 0 multphr(fun,hf,gf