Optimization MT (OPTMT)¶

An optimization package for GAUSS.

Description¶

OPTMT is intended for the optimization of functions. It has many features, including a wide selection of descent algorithms, step-length methods, and “on-the-fly” algorithm switching. Default selections permit you to use Optimization with a minimum of programming effort. All you provide is the function to be optimized and start values, and OPMT does the rest.

Installation¶

Please contact us with to request pricing and installation information.

If you already own OPTMT, you can install the library directly from within GAUSS using the GAUSS Package Manager .

Key Features¶

Descent methods¶

BFGS (Broyden, Fletcher, Goldfarb and Powell)
Steepest Descent
DFP (Davidon, Fletcher and Powell)
Newton

Line search methods¶

STEPBT
Brent’s method
Half
Strong Wolfe’s conditions

Advantages¶

Flexible¶

Bounded parameters.
Specify fixed and free parameters.
Dynamic algorithm switching.
Compute all, a subset, or none of the derivatives numerically.
Easily pass data other than the model parameters as extra input arguments. New!

Efficient¶

Threaded and thread-safe.
Option to avoid computations that are the same for the log-likelihood function and derivatives.
The tremendous speed of user-defined procedures in GAUSS speeds up your estimation.

Trusted¶

For more than 30 years, leading researchers have trusted the efficient and numerically sound code in the GAUSS optimization estimation tools to keep them at the forefront of their fields.

Available Optimization Controls¶

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

Control Options¶

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, Steepest descent, 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	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 OPTMT compute a numerical gradient using the forward, central, or backwards difference method.
Hessian Method	Either compute an analytical Hessian, or have OPTMT 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.

Basic Maximum Likelihood Estimation

User Guide