quasi-Newton-BFGS.rar_Quasi-Newton_optimization_quasi newton _re

function [s,phis,k,ds,dphi,S]=alpha_min(phi,a,b,delta,epsilon) %功能: 精确线搜索之抛物线法 %输入: phi 是目标函数, a和b是搜索区间的端点 % delta,epsilon是容许误差 %输出: s是近似极小点, phis是对应的近似极小值; % ds, dphi分别是s, phis的误差界; S是迭代向量 s0=a; maxj=20; maxk=30; big=1e6; err=1; k=1; S(k)=s0; cond=0; h=1; ds=0.00001; if (abs(s0)>1e4), h=abs(s0)*(1e-4); end while (k<maxk & err>epsilon &cond~=5) f1=(feval(phi,s0+ds)-feval(phi,s0-ds))/(2*ds); if(f1>0), h=-abs(h); end s1=s0+h; s2=s0+2*h; bars=s0; phi0=feval(phi,s0); phi1=feval(phi,s1); phi2=feval(phi,s2); barphi=phi0; cond=0; j=0; %确定h使得phi1<phi0且phi1<phi2 while(j<maxj&abs(h)>delta&cond==0) if (phi0<=phi1), s2=s1; phi2=phi1; h=0.5*h; s1=s0+h; phi1=feval(phi,s1); else if (phi2<phi1), s1=s2; phi1=phi2; h=2*h; s2=s0+2*h; phi2=feval(phi,s2); else cond=-1; end end j=j+1; if(abs(h)>big|abs(s0)>big), cond=5; end end if(cond==5) bars=s1; barphi=feval(phi,s1); else %二次插值求phis d=2*(2*phi1-phi0-phi2); if(d<0), barh=h*(4*phi1-3*phi0-phi2)/d; else barh=h/3; cond=4; end bars=s0+barh; barphi=feval(phi,bars); h=abs(h); h0=abs(barh); h1=abs(barh-h); h2=abs(barh-2*h); %确定下一次迭代的h值 if(h0<h), h=h0; end if(h1<h), h=h1; end if(h2<h), h=h2; end if(h==0), h=barh; end if(h<delta), cond=1; end if(abs(h)>big|abs(bars)>big), cond=5; end %迭代终止判别 err=abs(phi1-barphi); %e0=abs(phi0-barphi); e1=abs(phi1-barphi); e2=abs(phi2-barphi); %if(e0~=0 & e0<err), err=e0; end %if(e1~=0 & e1<err), err=e1; end %if(e2~=0 & e2<err), err=e2; end %if(e0~=0 & e1==0 & e2==0), err=0; end %if(err<epsilon), cond=2; end s0=bars; k=k+1; S(k)=s0; end if(cond==2&h<delta), cond=3; end end s=s0; phis=feval(phi,s); ds=h; dphi=err;