最速梯度法和牛顿法的步长的算法

  

   

    

     

    
    

     

      %  Program: inex_lsearch.m
     
    
   

    

     

    
    

     

      %  Title: Inexact Line Search
     
    
   

    

     

    
    

     

      %  Description: Implements Fletcher's inexact line search described in
     
    
   

    

     

    
    

     

      %  Algorithm 4.6.
     
    
   

    

     

    
    

     

      %  Theory: See Practical Optimization Sec. 4.8
     
    
   

    

     

    
    

     

      %  Input:
     
    
   

    

     

    
    

     

      %    x:  initial point
     
    
   

    

     

    
    

     

      %    s:  search direction
     
    
   

    

     

    
    

     

      %    F:  objective function to be minimized along the direction of s 
     
    
   

    

     

    
    

     

      %    G:  gradient of objective function F
     
    
   

    

     

    
    

     

      %   p1:  internal parameters that are required for the implementation of
     
    
   

    

     

    
    

     

      %        the line search regardless of the application at hand.
     
    
   

    

     

    
    

     

      %        It is a string (e.g. 'rho = 0.1') and can be a combination several
     
    
   

    

     

    
    

     

      %        internal parameters (e.g., 'rho = 0.25; sigma=0.5').
     
    
   

    

     

    
    

     

      %        Useful p1's include:                            default value
     
    
   

    

     

    
    

     

      %        'rho=   ' defines right bracket                      0.1
     
    
   

    

     

    
    

     

      %        'sigma= ' defines left bracket  (sigma >= rho)       0.1
     
    
   

    

     

    
    

     

      %        'tau= '   defines minimum step for se
     
    
  
 

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