Constrained Optimization MT

Constrained Optimization MT

COMT solves the Nonlinear Programming problem, subject to general constraints on the parameters - linear or nonlinear, equality or inequality, using the Sequential Quadratic Programming method in combination with several descent methods selectable by the user.

COMT’s ability to handle general nonlinear functions and nonlinear constraints along with other features, such as the Trust Region Method, allow you to solve a wide range of sophisticated optimization problems. Built on the speed and number crunching ability of the GAUSS platform, COMT quickly computes solutions to large problems, making it ideal for large scale Monte Carlo or Bootstrap optimizations.

Version 2.0 is easier to use than ever!

• New syntax options eliminate the need for PV and DS structures:
  • Decreasing the required code up to 25%.
  • Decreasing runtime up to 20%.
  • Simplifying usage.
• Optional dynamic arguments make it simple and transparent to add extra data arguments beyond model parameters to your objective function.
• Updated documentation and examples.
• Fully backwards compatible with COMT 1.0.
Platform: Windows, Mac, and Linux

Requirements: GAUSS/GAUSS Engine/GAUSS Light v16 or higher

Below is a full example for a simple nonlinear optimization problem.

//Make comt library available
library comt;

//Create data needed by objective procedure
Q = { 0.78 -0.02 -0.12 -0.14,
     -0.02  0.86 -0.04  0.06,
     -0.12 -0.04  0.72 -0.08,
     -0.14  0.06 -0.08  0.74 };

b = { 0.76, 0.08, 1.12, 0.68 };

//Objective procedure with 4 inputs:
//    i.      x       - The parameter vector
//    ii-iii. Q and b - Extra data needed by the objective procedure
//    ii.     ind     - The indicator vector
proc  qfct(x, Q, b, ind);
    //Declare 'mm' to be a modelResults
    //struct local to this procedure, 'qfct'
    struct modelResults mm;
   
    //If the first element of the indicator
    //vector is non-zero, compute function value
    //and assign it to the 'function' member
    //of the modelResults struct
    if ind[1];
        mm.function = 0.5*x'*Q*x - x'b;
    endif;
    
    //Return modelResults struct
    retp(mm);
endp;

//Starting parameter values
x_strt = { 1, 1, 1, 1 };

//Minimize objective function
struct comtResults out;
out = comt(&qfct,x_strt,Q,b);

//Print results held in comtResults structure
call comtPrt(out);

The above example will create the following report:

=============================
 COMT Version 2.0.0                         
=============================

Return code    = 0   
Function value = -2.17466  
Convergence    : normal convergence

Parameters  Estimates    Gradient
-----------------------------------
x[1,1]         1.5350      0.0000
x[2,1]         0.1220      0.0000
x[3,1]         1.9752      0.0000
x[4,1]         1.4130      0.0000


Number of iterations    16