MATLAB实现梯度下降算法(gradient descent)，案例丰富【数学建模、科学计算算法】.zip

%% %梯度下降算法(gradient descent) %说明：对一个二元多项式进行求最小值(x1,x2)——>min(fn) %时间：2016-01-04 %作者：zlw %% clc;clear;close all; syms x1 x2 r; fn=x1-x2+2*x1^2+2*x1*x2+x2^2;%定义函数 %exmp:fn0=subs(fn,{x1,x2},{1,2});%计算(1,2)处的函数值 dfn1=diff(fn,x1);%求x1偏导 dfn2=diff(fn,x2);%求x2偏导 e=0.000001;%误差范围 x_next=[0,0];%初始给定点 for k=1:10000 t1(k)=x_next(1);t2(k)=x_next(2); dfn=[subs(dfn1,{x1,x2},{t1(k),t2(k)}),subs(dfn2,{x1,x2},{t1(k),t2(k)})];%计算该点的偏导 d=-dfn; if d*d'<=e x_min=[t1(k),t2(k)];%输出最优点 break; else x_temp=[t1(k),t2(k)]+r*d; yr=subs(fn,{x1,x2},{x_temp(1),x_temp(2)}); dyr=diff(yr,r); r_min=double(solve(dyr,r)); %(求最优步长r)导数为0时的r值,solve求等式方程很强大 x_next=[t1(k),t2(k)]+r_min*d; end end disp('最小值点(x1,x2)为：'); disp(x_min); disp('最小值为：') disp(double(subs(fn,{x1,x2},x_min)));