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 <https://www.aptech.com/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 <https://www.aptech.com/blog/gauss-package-manager-basics/>`_ .

Requires GAUSS/GAUSS Engine/GAUSS Light v16 or higher.

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
+++++++++++++++++++++++++++++++

.. list-table::
    :widths: auto

    * - 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.


.. toctree::
    :maxdepth: 2
    :hidden:
    :caption: Optimization Documents

    user-guide
    command-reference
    optmt-examples