OPTIMIZATION MT 2.0

OPMT 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.

 

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 OPTMT 1.0

 

KEY FEATURES

DETAILS

Novice users will typically leave most of these options at the default values. However, they 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
DESCENT ALGORITHMS	BFGS, DFP, Newton and Steepest Descent.
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.

 

© 2024 Aptech Systems, Inc. All rights reserved.

 

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.

 

The code below finds the minimum of the simple function x². The objective function in this case computes the function value and/or the gradient, depending upon the value of the incoming indicator vector, ind. This makes it simple to avoid duplication of calculations which are required for the objective function and the gradient when computing more complicated functions.