Constrained Optimization MT (COMT)

A constrained optimization package for GAUSS.


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.


Please contact us with to request pricing and installation information.

If you already own COMT, you can use the GAUSS Package Manager to install COMT as well.

Key Features

Descent methods

  • BFGS (Broyden, Fletcher, Goldfarb and Powell)

  • Modifed BFGS

  • DFP (Davidon, Fletcher and Powell)

  • Newton-Raphson

Line search methods

  • Augmented trust region method


  • Brent’s method

  • Half

  • Strong Wolfe’s conditions

Constraint types

  • Linear equality and inequality constraints

  • Nonlinear equality and inequality constraints

  • Bounded parameters

Available Optimization Controls

Optimization controls are set to default values that few users ever need to change. However, COMT is fully customizable and the flexible optimization options can be a great help when tackling more difficult problems.

Control Options

Linear equality constraints

Optional, simple to specify, linear equality constraints.

Linear inequality constraints

Optional, simple to specify, linear inequality constraints.

Nonlinear equality constraints

Option to provide a procedure to compute nonlinear equality constraints.

Nonlinear inequality constraints

Option to provide a procedure to compute nonlinear inequality constraints.

Parameter bounds

Simple parameter bounds of the type: lower_bd ≤ x_i ≤ upper_bd.

Feasible test

Controls whether parameters are checked for feasibility during line search.

Trust radius

Set the size of the trust radius, or turn off the trust region method.

Descent algorithms

BFGS, Modified BFGS, DFP, and Newton.

Algorithm switching

Specify descent algorithms to switch between based upon the number of elapsed iterations, a minimum change in the objective function, or line search step size.

Line search method

Augmented Lagrangian Penalty, STEPBT (quadratic and cubic curve fit), Brent’s method, half-step, or Strong Wolfe’s Conditions.

Active parameters

Control which parameters are active (to be estimated) and which should be fixed to their start value.

Gradient Method

Either compute an analytical gradient, or have COMT compute a numerical gradient using the forward, central, or backwards difference method.

Hessian Method

Either compute an analytical Hessian, or have COMT compute a numerical Hessian using the forward, central, or backwards difference method.

Gradient check

Compares the analytical gradient computed by the user-supplied function with the numerical gradient to check the analytical gradient for correctness.

Random seed

Starting seed value used by the random line search method to allow for repeatable code.

Print output

Controls whether (or how often) iteration output is printed and whether a final report is printed.

Gradient step

Advanced feature: Controls the increment size for computing the step size for numerical first and second derivatives.

Random search radius

The radius of the random search if attempted.

Maximum iterations

Maximum iterations to converge.

Maximum elapsed time

Maximum number of minutes to converge.

Maximum random search attempts

Maximum allowed number of random line search attempts.

Convergence tolerance

Convergence is achieved when the direction vector changes less than this amount.