Summary
Function minimization routines.
Description
Introduces the following algorithms for finding the minimum of scalar function of several variables:
- Nelder-Mead (Simplex); unconstrained and bounded minimization.
- Quasi-Newton (BFGS or DFP update scheme); unconstrained minimization.
- Levenberg-Marquardt (Marquardt); unconstrained minimization.
- Conjugate Gradient (Fletcher - Reeves or Polak - Ribiere update scheme); unconstrained minimization.
Introduces the following algorithms for finding the minimum of vector function of several variables:
- Trust Region (TR); unconstrained and bounded minimization.
Introduces the following algorithms for finding the minimum of function of single variable:
- Brent method; unconstrained minimization.
In addition, several routines for linear programming (LP) are also provided. The following algorithms are supported:
- Two phase Simplex method.
- Dual Simplex method.
- Simplex method.
- Gomory's cutting plane algorithm for solving integral problems.
Types
| Name | Summary |
|---|
| TEPSArray | Stores the stopping tests for TR optimization. |
| TGrad | Defines the procedure for calculating the gradient of a real function. |
| TGradHess | Defines the procedure for calculating the gradient and Hessian matrix of a real function. |
| TJacobianFunction | Defines procedure for calculating the jacobian matrix. |
| TLPAlgorithm | Linear programming algorithm. |
| TLPSolution | LP system solution. |
| TOptMethod | Optimization methods. |
| TOptStopReason | Why the main loop in optimization stopped. |
| TVectorFunction | Defines vector function of several variables. |
Routines
| Name | Summary |
|---|
| BFGS | Minimizes the function of several variables by using the Quasi-Newton optimization algorithm. |
| ConjGrad | Minimizes the function of several variables by using the Conjugate gradient optimization algorithm. |
| CPA | Gomory's cutting plane algorithm for solving the integer programming problem. |
| Marquardt | Minimizes the function of several variables by using the Marquardt optimization algorithm. |
| MinBrent | Minimizes single variable function. |
| Simplex | Minimizes the function of several variables by using the Nelder-Mead (Simplex) optimization method. |
| SimplexDual | Linear optimization by Dual Simplex algorithm. |
| SimplexLP | Linear optimization by using Simplex method. |
| SimplexTwoPhase | Linear optimization by Two-Phase Simplex algorithm. |
| TrustRegion | Trust region algorithm for finding minimum of vector function. |
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