大连理工优化方法增广拉格朗日方法MATLAB程序.docVIP

上机大作业II 定义目标函数fun function f=fun(x) x1=x(1); x2=x(2); f=4*x1-x2^2-12; 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)^2-x(2)^2; 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)^2+10*x(2)-x(2)^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mpsi function 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; end psi=psi+0.5*sigma*s1; s2=0.0; for i=1:m s3=max(0.0, lambda(i) - sigma*gi(i)); s2=s2+s3^2-lambda(i)^2; end psi=psi+s2/(2.0*sigma); 定义增广拉格朗日函数梯度函数dmpsi function 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); end for i=1:m dpsi=dpsi+(sigma*gi(i)-lambda(i))*dgi(:,i); end 定义BFGS法函数函数bfgs function [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=-Bk\gk; m=0; mk=0; while(m20) newf=feval(mpsi,x0+rho^m*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*rho^m*gk*dk) mk=m; break; end m=m+1; end x=x0+rho^mk*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; end val=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multphr function answer=multphr