plus_step_search.m

无约束优化问题一维搜索的常用方法：黄金分割法（golden_section.m）、加步搜索法（plus_step_search.m）、牛顿法（newton.m）、抛物线法（parabola.m）

function [vec,times,minip]=plus_step_search(str,ini,step,multiple)
%  File name:plus_step_search.m      
%  Author:Yan Anxin
%  ID number:081810
%  Date:finished on 2008.11.24
%  Description:  
%       Here defines a function,to determine the initial search interval by plus-step-search-method
%       In the syntax [vec,times,minip]=plus_step_search(str,ini,step,multiple),
%       str----input,means the expression of objective function
%       ini----input,sets the initial searching point to ini 
%       step----input,sets initial searching step
%       multiple----input,sets multiple of the plusing step
%       vec=plus_step_search(str,ini,step,multiple) attempts to find vec, i.e. the initial search interval
%       [vec,times]=plus_step_search(str,ini,step,multiple) returns times, i.e. the times of iterative   
%       [vec,times,minip]=plus_step_search(str,ini,step,multiple) returns minip, i.e. the minimum of sorting point  
 
f=sym(str);
syms x
times=0;h(1)=step;                  %setting initial value
y(1)=ini;y(2)=y(1)+h(1);

if subs(f,x,y(2))<subs(f,x,y(1))    %searching forward
    k=3;
    while 1
        h(k-1)=h(k-2)*multiple;times=times+1;
        y(k)=y(k-1)+h(k-1);
        if subs(f,x,y(k))>=subs(f,x,y(k-1)),break,end
        k=k+1;
    end
else                                %searching backward 
    y(3)=y(1)-h(1);k=3;
    while subs(f,x,y(k))<subs(f,x,y(k-1))
        k=k+1;times=times+1;
        h(k-2)=h(k-3)*multiple; 
        y(k)=y(k-1)-h(k-2);                
    end    
end
y(k+1)=0.5*(y(k)+y(k-1));           %sorting of four points
b=[k-2:k-1 k+1 k];
B=[subs(f,x,y(b))];
[C,D]=min(B);
if y(b(D-1))<=y(b(D+1)),vec=y(b([D-1 D+1]));else vec=[y(b(D+1)) y(b(D-1))];end
minip=y(b(D));