對分法求解目標函數(shù)最優(yōu)解函數(shù)MATLAB實現(xiàn)(共4頁)

1、%對分法求解目標函數(shù)最優(yōu)解函數(shù)function t,y= equation_extremum (x,a,b,epsional)%=%函數(shù)默認參數(shù)：%x為目標函數(shù)，輸入字符串型，默認最優(yōu)解求其最小值%a，b為其初始區(qū)間，默認閉區(qū)間，a<b%對初始區(qū)間的要求：初始區(qū)間是單谷區(qū)間，函數(shù)求極小值%則a處的導數(shù)<=0,b處的導數(shù)>=0;%=syms t;x_inline=inline(sym(x);func_diff=diff(sym(x);func_diff_inline=inline(func_diff);t=b;high_value=func_diff_inline(t);t=a

2、;low_value=func_diff_inline(t);if high_value*low_value>0 t='本函數(shù)不可解' y='給定初始區(qū)間非單谷區(qū)間'else if high_value*low_value=0 if high_value=0 t=b; y=x_inline(t); else t=a; y=x_inline(t); end else while abs(high_value-low_value)>=epsional; c=1/2*(b+a); t=c; middle_value=func_diff_inline(t);

3、 if middle_value>0 high_value=middle_value; b=c; else if middle_value<0 low_value=middle_value; a=c; else if middle_value=0 break; end end end end c=1/2*(b+a); t=c; y=x_inline(t); endend運行代碼：%=close all;clear all;clc;%目標函數(shù)syms t;t,y=equation_extremum('t*(t-3)',t,-3,5,0.1);disp(t,y);運行結

4、果：t=1.5y=-2.25%拋物線法求函數(shù)最優(yōu)解function t,y=parabola_extremum(x,t1,t2,epsional)%=%函數(shù)默認參數(shù)：%x為目標函數(shù)，輸入字符串型，例如：'x2-sin(x)'默認最優(yōu)解求其最小值%a，b為其初始區(qū)間，默認閉區(qū)間，t1<t2%對初始區(qū)間的要求：初始區(qū)間是單谷區(qū)間，函數(shù)求極小值%=syms t;x_inline=inline(sym(x);%生成隨機數(shù)求出t0；high_value=x_inline(t2);low_value=x_inline(t1);t0=parabola_overture(x,t,t1,t

5、2);%自定義函數(shù)，試探法求t0middle_value=x_inline(t0);%擬合曲線，待定系數(shù)法%p(t0)=a0+a1*t0+a2*t02=f(t0)%p(t1)=a0+a1*t1+a2*t22=f(t1)%p(t2)=a0+a1*t2+a2*t22=f(t2)%推出：%a1=(t02-t22)*f(t1)+(t22-t12)*f(t0)+(t12-t02)*f(t2)/(t1-t0)*(t0-t2)*(t2-t1)%a2=(t0-t2)*f(t1)+(t2-t1)*f(t0)+(t1-t0)*f(t2)/(t1-t0)*(t0-t2)*(t2-t1)while 1t_ba=0.5

6、*(t02-t22)*low_value+(t22-t12)*middle_value+(t12-t02)*high_value)/(t0-t2)*low_value+(t2-t1)*middle_value+(t1-t0)*high_value);t_ba_value=x_inline(t_ba);if abs(t_ba-t0)<epsional t=t_ba; y=t_ba_value; break;else if t_ba>t0 if t_ba_value<=middle_value t1=t0; t0=t_ba; low_value=middle_value; mid

7、dle_value=t_ba_value; else t2=t_ba; high_value=t_ba_value; end else if t_ba_value<=middle_value t2=t0; t0=t_ba; high_value=middle_value; middle_value=t_ba_value; else t1=t_ba; low_value=t_ba_value; end endenddisp(t1,t0,t2;low_value,middle_value,high_value)end%試探法求函數(shù)低點值，用于拋物線插值法function t0=parabol

8、a_overture(x,a,b)%=%函數(shù)默認參數(shù)：%x為目標函數(shù)，輸入字符串型，例如：'x2-sin(x)'%a，b為其初始區(qū)間，默認閉區(qū)間，a<b%對初始區(qū)間的要求：初始區(qū)間是單谷區(qū)間，函數(shù)求極小值%=syms t;x_inline=inline(sym(x);%生成隨機數(shù)求出t0；rand_t0=rand(1,10);high_value=x_inline(b);low_value=x_inline(a);middle_value=x_inline(rand_t0(1);k=1;while middle_value>high_value|middle_value>low_value k=k+1; middle_value=x_inline(rand_t0(k); if k>50 printf('請重新運行程序'); break; endendt0=rand_t0(k);運行代碼:close all;clear all;clc