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MathGroup Archive 1995

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Re: projected gradient

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg1620] Re: projected gradient
  • From: "James Albert Larson" <larso171 at maroon.tc.umn.edu>
  • Date: Thu, 6 Jul 1995 23:23:00 -0400
  • Organization: University of Minnesota, Twin Cities

On 2 Jul 1995 22:59:29 GMT, 
Filippo  <teltesi25 at .polito.it> wrote:

>I am an Electrical Engineering Student needing to find 
>the constrained minimum of a function of several
>variables using the projected gradient algorithm.
>I would like to know if this algorithm is already
>been inplemented for Mathematica and should this be
>the case how to find it.

Ans: no.  The LinearProgramming and ConstrainedMin works with 
constraints, but is only for linear objective function and linear 
constraints.  The only other optimization function in Mathematica is 
FindMinimum -- the objective function can be nonlinear, but no constraints 
are allowed.  (There are also ConstrainedMax and FindMaximum -- the same as 
ConstrainedMin and FindMinimum except maximizes rather than minimizes).

This is the only thing I am aware of from Mathsource or anywhere else that 
deals with constrained nonlinear problems:

MultiplierMethod -- A General 
Purpose Algorithm forNonlinear Programming

Jean-Christophe Culioli

Revision date: 950116 

This is an implementation of the Method of Multipliers (or the Augmented 
Lagrangian method) due to Hestenes, Powell, Rockafellar and others. It 
solves nonlinear programming minimization problems with inequality and/or 
equality constraints. As such, it is a natural generalization of the 
FindMinimum built-infunction. See for example D. G. Luenberger, "Linear 
and Nonlinear Programming", Addison-Wesley,second. ed., 1989. See also D. 
P. Bertsekas, "Constrained Optimization and Lagrange MultiplierMethods", 
Academic Press, 1982. 

        MultiplierMethod.m Mathematica package (940917, 9 Kb) 
        MultiplierMethod.ma Mathematica notebook (940917, 19 Kb) 

Jim Larson



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