有限记忆算法_用于处理大规模算法_算法原理为把不断迭代的牛顿矩阵分解并部分抵消达到减少运算量_matlab

function [x0,val,k]=lsnCG(x0,m,n,t) s=zeros(t,m); y=zeros(t,m); kmax=2000; epsilon=1e-05; for k=1:kmax r0=gfun(x0,n); %梯度方向 if norm(r0)<epsilon break; end if k==1 p0=-r0; elseif k<=m H0=s(:,k-1)'*y(:,k-1)/(y(:,k-1)'*y(:,k-1))*eye(t,t); [p0]=LM(r0,s,y,m,H0,k); %方向 p0=-p0; else H0=s(:,m)'*y(:,m)/(y(:,m)'*y(:,m))*eye(t,t); [p0]=LM(r0,s,y,m,H0,k); %方向 p0=-p0; end alph=0.5; rho=1/4; sigma=0.5; jmax=200; f0=fun0(x0,n); for j=1:jmax % armijo搜索步长 x1=x0+alph*p0; if (fun0(x1,n)<=f0+sigma*r0'*alph*p0) break; else alph=alph*rho; end end gfun1=gfun(x1,n); if k<=m s(:,k)=x1-x0; y(:,k)=gfun1-r0; else for i=1:min(m-1,k-1) s(:,i)=s(:,i+1); y(:,i)=y(:,i+1); end s(:,m)=x1-x0; y(:,m)=gfun1-r0; end x0=x1; end val=fun0(x0,n); val=double(val); end