信赖域算法matlab实现

%syms s t; %f=(t+3)^2+(t-2*s)^2; %[xm,minf]=minTruA(f,[0 0],0.1,0.3,0.7,[t s]) %Optimization terminated: no negative curvature detected in current % trust region model and first order optimality measure < OPTIONS.TolFun. %Optimization terminated: relative function value changing by % less than OPTIONS.TolFun. %Optimization terminated: no negative curvature detected in current % trust region model and first order optimality measure < OPTIONS.TolFun. %Optimization terminated: no negative curvature detected in current % trust region model and first order optimality measure < OPTIONS.TolFun. %Optimization terminated: relative function value changing by % less than OPTIONS.TolFun. %Optimization terminated: relative function value changing by %less than OPTIONS.TolFun. %xm = % % -3.0000 % -1.5000 % % %minf = % % 1.9722e-031 function [x,minf]=minTruA(f,x0,r0,mu,yita,var,eps) %目标函数:f; %初始点：x0； %初始信赖域半径：r0； %初始参数：mu %初始参数：yita %自变量向量：var； %精度：eps； %目标函数取最小值的自变量值：x； %目标函数的最小值：minf if nargin==6 eps=1.0e-6; end tol=1; x0=transpose(x0); r=r0; while tol>eps gradf=jacobian(f,var); jacf=jacobian(gradf,var);%雅可比矩阵 fx=Funval(f,var,x0); v=Funval(gradf,var,x0); pv=Funval(jacf,var,x0); tol=norm(v); H=double(pv);%二次规划 中的二次项矩阵 c=transpose(v);%二次规划 中的一次项矩阵 lb=-r*ones(length(var),1);%r为信赖域半径，自变量下界约束 ub=r*ones(length(var),1);%自变量上界约束 [y,fy]=quadprog(H,c,[],[],[],[],lb,ub);%求解二次规划 fx_n=Funval(gradf,var,x0+y); p=(fx-fx_n)/(-fy); if p<= mu %修改信赖域半径 r=0.5*r; else x0=x0+y; if p>=yita r=2*r; end end end x=x0; minf=Funval(f,var,x); format short;