非线性规划的序列二次规划（SQP）算法Matlab程序

clear;clc; rho = 0.5; xold=rho*ones(2,1); xold=[1.23;3.45] beta=0.6;eta=1e-3;sigmabar=1;sigma=1;nmax=500;epsilon=1e-6; nit=0;nf=0;nc=0;ngf=0;ngc=0; fxold=funf(xold);nf=nf+1; gfxold=gradf(xold);ngf=ngf+1; hxold=funh(xold);nc=nc+1; ghxold=gradh(xold);ngc=ngc+1; vxold=funv(xold);n=length(xold);m=length(hxold);Bk=eye(n); flag = 2; OPTIONS = optimoptions('quadprog','Display','off'); while nit<=nmax [dk,~,~,~,Lambda] = quadprog(Bk,gfxold,[],[],ghxold',-hxold,[],[],[],OPTIONS); lambda = Lambda.eqlin; if norm(dk)<=epsilon flag=0;break; end sigma1=norm(lambda,1)+sigmabar; if sigma<sigma1 sigma=max(sigma1,1.5*sigma); end barP_sigma=fxold+gfxold'*dk+0.5*dk'*Bk*dk; P_sigmaxold=fxold+sigma*vxold; alpha=1; while alpha>1e-10 xnew=xold+alpha*dk;fxnew=funf(xnew);nf=nf+1; hxnew=funh(xnew);nc=nc+1; vxnew=funv(xnew); P_sigmaxnew=fxnew+sigma*vxnew; if P_sigmaxnew-P_sigmaxold<=eta*alpha*(barP_sigma-P_sigmaxold) break; end alpha=beta*alpha; end if alpha<=1e-10 flag=1;fprintf('步长太小',alpha);break; end s=xnew-xold; gfxnew=gradf(xnew);ghxnew=gradh(xnew);ngf=ngf+1;ngc=ngc+1; q=gfxnew+ghxnew*lambda-(gfxold+ghxold*lambda); bfail=1;[Bk,bfail]=bfgs(Bk,s,q,n,bfail); fprintf('dk=%4d, alpha=%.4f, sigma=%d, fxold=%.4f, vxold=%4d\n',norm(dk),alpha,sigma,fxold,vxold) xold=xnew;fxold=fxnew;gfxold=gfxnew;hxold=hxnew;ghxold=ghxnew; vxold=vxnew;nit=nit+1; end nit,fxold,xold,vxold,flag