CG程序代码function [x,y] = cg(A,b,x0) %%%%%%%%%%%%%%%%%CG算法%%%%%%%%%%%% r0 = A*x0-b;p0 = -r0;k = 0;r = r0;p = p0;x = x0;while r~=0alpha = -r'*p/(p'*A*p);x = x+alpha*p;rold = r;r = rold+alpha*A*p;beta = r'*r/(rold'*rold);p = -r+beta*p;plot(k,norm(p),'.--');hold onk = k+1;endy.funcount = k;y.fval = x'*A*x/2-b'*x;function [x,y] = cg_FR(fun,dfun,x0)%%%%%%%%%%%%%%%CG_FR算法%%%%%%%%%%%%%%%error = 10^-5;f0 = feval(fun,x0);df0 = feval(dfun,x0);p0 = -df0;f = f0;df = df0;p = p0;x = x0;k = 0;while ((norm(df)>error)&&(k<1000))f = feval(fun,x);[alpha,funcNk,exitflag] = lines(fun,0.01,0.15,0.85,6,f,df'*p,x,p);%%用线搜索找下降距离%% if exitflag == -1disp('Break!!!');break;endx = x+alpha*p;dfold = df;df = feval(dfun,x);beta = df'*df/(dfold'*dfold);p = -df+beta*p;plot(k,norm(df),'.--');hold onk = k+1;endy.funcount = k;y.fval = feval(fun,x);y.error = norm(df);function [x,output] = bfgs(fun,dfun,x0,varargin) %%%%%%%%%%%优化课程BFGS算法程序%%%%%%%%%%%epsi = 1.0e-6;k = 0;funcN = 0;rho = 0.01;l = 0.15;u = 0.85;x = x0;f = feval(fun,x,varargin{:});funcN = funcN + 1;n = length(x0);H = eye(n);g = feval(dfun,x,varargin{:});while norm(g)>epsi && k<=1000itercon = true;d = -H*g;alpha_0 = 1;gd = g'*d;[alpha,funcNk,exitflag] = lines(fun,rho,l,u,alpha_0,f,gd,x,d,varargin{:});funcN = funcN + funcNk;if exitflag == -1itercon = false;restart = true;H = eye(n);gold = g;endif itercons = alpha*d;x = x + s;f = feval(fun,x,varargin{:});funcN = funcN + 1;gold = g;g = feval(dfun,x,varargin{:});y = g - gold;hy = H*y;sy = s'*y;yhy = y'*hy;if sy<0.2*yhytheta = 0.8*yhy/(yhy-sy);s = theta*s + (1 - theta)*hy;sy = 0.2*yhy;endv = sqrt(yhy)*(s/sy - hy/yhy);H = H + s*s'/sy - hy*hy'/yhy + v*v';endk = k + 1;endoutput.fval = f;output.iteration = k;output.funcount = funcN;output.gnorm = norm(g);function [x,output] = newton_cg(fun,dfun,ddfun,x0) %%%%%%%%%%%%%%优化7.1算法程序%%%%%%%%%%%%%%%%%n = length(x0);x = x0;k = 1;d(1,1:n) = zeros(1,n);%%%%%%%%%循环开始，直至满足条件结束%%%%%%%%%%while (norm(feval(dfun,x))>=10^-5)&&(k<20000)epsi(k) = min(0.5,sqrt(norm(feval(dfun,x))))*norm(feval(dfun,x));z(1,1:n) = zeros(1,n);B = feval(ddfun,x);r(1,1:n) = feval(dfun,x)';d(1,1:n) = -r(1,1:n);p = zeros(1,n)';for j=1:k %%%%%%%%寻找最优下降方向%%%%%%%%%if d(j,1:n)*B*d(j,1:n)'<=0if j==1p = -r(k,1:n)';break;elsep = z(j,1:n)';break;endendalpha = r(j,1:n)*r(j,1:n)'/(d(j,1:n)*B*d(j,1:n)');z(j+1,1:n) = z(j,1:n) + alpha*d(j,1:n);r(j+1,1:n) = r(j,1:n) + alpha*(B*d(j,1:n)')';if norm(r(j+1,1:n))<epsi(k)p = z(j+1,1:n)';break;endbeta = r(j+1,1:n)*r(j+1,1:n)'/(r(j,1:n)*r(j,1:n)');d(j+1,1:n) = -r(j+1,1:n) + beta*d(j,1:n);end %%%%%%%%%%方向找寻结束%%%%%%%%%%%%%%%%%%%%%%获得新的迭代点%%%%%%%%%%%gd = -d(1,1:n)*d(1,1:n)';[alpha1,funcNk,exitflag] = lines(fun,0.01,0.15,0.85,1,feval(fun,x),gd,x,d(1,1:n)');x = x + alpha1*p;k = k + 1;endoutput.fval = feval(fun,x);output.funcount = k;function [x,output] = cg_steihaug(fun,dfun,ddfun,x0)%%%%%%%%%%%优化7.2算法程序%%%%%%%%%%%%%%%%%%%%%%参数初始化%%%%%%%%%%%n = length(x0);x = x0;k = 1;d(1,1:n) = zeros(1,n);%%%%%%%%%%开始循环，直至满足条件%%%%%%%%%%%while (norm(feval(dfun,x))>=10^-5)&&(k<2000)epsi(k) = min(0.5,sqrt(norm(feval(dfun,x))))*norm(feval(dfun,x));z(1,1:n) = zeros(1,n);B = feval(ddfun,x);r(1,1:n) = feval(dfun,x)';d(1,1:n) = -r(1,1:n);delta(k) = 1;%%%%%%%%%p = [0,0]';%%%%%%%%%%%%%开始搜索最优下降方向%%%%%%%%%%%%%%%%%%%%%%%%%%%%此算法利用信赖域法寻找方向%%%%%%%%%%%%%%%if norm(r(1,1:n))<epsi(k)p = z(1,1:n)';break;endfor j=1:kif d(j,1:n)*B*d(j,1:n)'<=0%delta(k)[s,val,posdef,count,lambda] = trustM(r(k,1:n)',B,delta(k));p = s;break;endalpha = r(j,1:n)*r(j,1:n)'/(d(j,1:n)*B*d(j,1:n)');z(j+1,1:n) = z(j,1:n) + alpha*d(j,1:n);if(norm(z(j+1,1:n))>=delta(k))%tao =(-4*z(j,1:n)*d(j,1:n)'+sqrt((2*z(j,1:n)*d(j,1:n)')^2-4*(z(j,1:n)*z(j,1:n)'-delta(k)^2)))/(2*d(j,1:n)*d(j, 1:n)');p = z(j,1:n)' + tao*d(j,1:n)';break;endr(j+1,1:n) = r(j,1:n) + alpha*(B*d(j,1:n)')';if norm(r(j+1,1:n))<epsi(k)p = z(j+1,1:n)';break;endbeta = r(j+1,1:n)*r(j+1,1:n)'/(r(j,1:n)*r(j,1:n)');d(j+1,1:n) = -r(j+1,1:n) + beta*d(j,1:n);end%%%%%%%%%%%下降方向搜索结束%%%%%%%%%%%%%%%%%%%%%%%%获得新的迭代点%%%%%%%%%%%%%%gd = -d(1,1:n)*d(1,1:n)';[alpha1,funcNk,exitflag] = lines(fun,0.01,0.15,0.85,1,feval(fun,x),gd,x,d(1,1:n)');x = x + alpha1*p;k = k + 1;endoutput.fval = feval(fun,x);output.funcount = k;。
