非线性算法合集（nonlinear algorithm）

包括牛顿拉夫逊法，Broyden拟牛顿法，弧长法，割线法。每种算法都包含有线性搜索迭代改进。

%%%%%%%%  ArcLength
clc;clear all;close all;
%%%%%%%%  parameter setting
b=0.5;
da=0.2;
d0=[0 0]‘;
lamda0=0;
maxit=2e2;
Fext=[40 15]‘;
ddata（:1）=d0;
lamdadata（:1）=lamda0;
l=1;
Kb=[10 1.2*d0（2）^2-10*d0（2）
     1.2*d0（1）^2-6*d0（1） 10];
q=Kb\Fext;
c=（1-b）/（q‘*Kb*q）;
while lamda0<=2 %&& abs（2-lamda0）>1e-10  %%%iteration loop 
    l;
    K0=[10 1.2*d0（2）^2-10*d0（2）
        1.2*d0（1）^2-6*d0（1） 10];
    if min（eig（K0））<=0 && max（eig（K0））<=0
        dlamda1=-da;
    else
        dlamda1=da;
    end
    %dlamda1=da;
    lamda1=lamda0+dlamda1;
    Fint=[10*d0（1）+0.4*d0（2）^3-5*d0（2）^2 
         0.4*d0（1）^3-3*d0（1）^2+10*d0（2）];  
    R0=lamda1*Fext-Fint;    
    dd1=dlamda1*inv（Kb）*Fext;
    d1=d0+dd1;    
    convg=0;
    tol=1e-10;
    it=0;
    while ~convg  %%%iteration loop 
        it=it+1;               
        f=sqrt（c*dd1‘*Kb*dd1+b*dlamda1^2）;
        Fint=[10*d1（1）+0.4*d1（2）^3-5*d1（2）^2 
              0.4*d1（1）^3-3*d1（1）^2+10*d1（2）];  
        K1=[10 1.2*d1（2）^2-10*d1（2）
            1.2*d1（1）^2-6*d1（1） 10];
        R1=lamda1*Fext-Fint;
        A=c/f*dd1‘*Kb*inv（K1）;
        B=lamda1*Fext-Fint;
        C=da-f;
        %Formula:  A（B+Dlamda1*Fext）+b/f*dlamda1*Dlamda1=C
        Dlamda1=（C-A*B）/（A*Fext+b/f*dlamda1）;
        Dd1=inv（K1）*（R1+Fext*Dlamda1）;
        d2=d1+Dd1;
        lamda2=lamda1+Dlamda1;
        dd2=dd1+Dd1;
        dlamda2=dlamda1+Dlamda1;
        
        dd1=dd2;
        d1=d2;
        lamda1=lamda2;        
        dlamda1=dlamda2;        
        Dd1‘*R1;
        if abs（R1）<=tol
            %fprintf（‘Iteration successes\n‘）;
            convg=1;                       
        end  
        
        if it>maxit
            convg=1;
            fprintf（‘need more iteration\n‘）;
        end        
        
    end    
    
    itdata（l1）=it;
    ddata（:l+1）=d1;
    lamdadata（:l+1）=lamda1;
    d0=d1;
    lamda0=lamda1;
    l=l+1;
end
figure1 = figure（‘Color‘[1 1 1]）;
NR=[00.2037683279785300.4196560185962490.6572930395651470.9340727627752981.291964870125211.953281568938114.856399586572535.191428089454325.439801081847235.643128197920805.817987126430115.972913055941036.112962027539086.241412019238086.360527677402146.471949652721466.576911411963036.676368492185056.771079823005516.861661192430886.948621722324327.032389563559347.113330527087667.191761966324667.267963408229547.342184938373137.414654044183927.485581437523357.555166273499537.623601137849607.691077185720717.757789890153477.823946029528287.889772877874587.955531207961718.021535006955488.088183541030518.156017720898888.225829027081088.29889836160529;00.08711802852429980.1998771076197100.3432513206388360.5291487400889560.7894914409041991.296497765071453.018932124196313.088725992871123.113569761699433.115275566367303.102376414683863.079195239606693.048250306197143.011143068263922.968953927204212.922442114589512.872156074300112.818498614

 属性            大小     日期    时间   名称
----------- ---------  ---------- -----  ----
     文件        4907  2014-10-21 11:57  BFGSLineNRLineNRBFGS.m
     文件        4666  2014-10-21 11:41  BroydenLineNRLine.m
     文件        2882  2014-10-21 09:49  ModifiedNewtonLinesearch.m
     文件        2625  2014-10-21 11:11  NewtonRaphsonLinesearch.m
     文件        3993  2014-10-21 12:31  ArcLength.m