Simplemax uses open source solvers.  Descriptions and links 
        to documentation and source code follow.  


                          BFGS Quasi-Newton - source - documentation
                                         
        quasi-Newton method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS).
        
        Optimize the function, f, whose gradient is given by fprime using the
        quasi-Newton method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS)
        See Wright, and Nocedal 'Numerical Optimization', 1999, pg. 198.

        
        
                          COBYLA - source - documentation
                                         
        Constrained Optimization BY Linear Approximation (COBYLA) method.
        
        "A direct search optimization method that models the objective and 
        constraint functions by linear interpolation", in 
        Advances in optimization and numerical analysis, Proceedings
	of the Sixth workshop on Optimization and Numerical Analysis, Oaxaca,
	Mexico, volume 275 of Mathematics and its Applications, pp 51--67.
	Kluwer Academic Publishers, 1994.
	
         
                
                          Conjugate Gradient - source - documentation
                                         
        Nonlinear Conjugate Gradient Algorithm.
        
        Optimize the function, f, whose gradient is given by fprime using the
        nonlinear conjugate gradient algorithm of Polak and Ribiere
        See Wright, and Nocedal 'Numerical Optimization', 1999, pg. 120-122.



                          Galileo - source - documentation
                                         
        Galileo is a global solver, and requires upper and lower bounds.  It 
        does not use an initial point and cannot handle Ax <= b constraints.
        
        This Genetic Algorithm-based solver was written by Donald Goodman. 
        


                   Modified Powell's method - source - documentation
                                       
        Powell's method, in any number of dimensions.

        Powell's Method begins with N directions, using a line minimization 
        method.  At each iteration the direction in which the function made its 
        largest decrease is discarded.
         
        xtol -- acceptable relative error in xopt for convergence.  
        ftol -- acceptable relative error in func(xopt) for convergence. 
      
        Powell, M. J. D., "An Efficient Method for Finding the Minimum of a 
        Function of Several Variables without Calculating Derivatives," 
        The Computer Journal, 1964, Vol. 7, p. 155
        
        
        
                             Ralg - source - documentation

        R-algorithm with adaptive space dilation.
        
        "Shor's r-algorithm is an iterative method for unconstrained optimization, 
        designed for minimizing nonsmooth functions, for which its reported 
        success has been considerable."
        
        Burke, J.V. et al., "The Speed of Shor's R-Algorithm", Submitted to IMA J. 
        Numer. Anal., 2007 
        (http://www.optimization-online.org/DB_HTML/2007/05/1656.html)
        

        
                     Nelder-Mead Simplex - source - documentation
                                         
        Downhill Simplex method, in any number of dimensions.
        
        A simplex in n-dimensions consists of n+1 distinct vertices.  The method 
        involves moving a simplex downhill, or if that is not possible, shrinking 
        its size.  The method is not highly efficient, and is appropriate only 
        for small numbers of variables (usually fewer than 6), but is robust. 
        
        xtol -- acceptable relative error in xopt for convergence.  
        ftol -- acceptable relative error in func(xopt) for convergence. 
        
        J.A. Nelder and R. Mead, The Computer Journal, 1965, Vol. 7, pp 308-313