A Mathematical/Statistical Control/Component by WebCab Components

This suite includes the following features:

Local unidimensional optimization - finds global minima / maxima for continuous functions in one dimension

Fast `low level' algorithms - use these algorithms when your primary concern is the speed and not the accuracy of the results. You will have to chose one bracketing algorithm and one locate algorithm (note, they are useful only in pairs). Also you will have to manually provide a lot of parameters (tolerance, maximum cycles etc) which can dramatically change the algorithm performance

Bracketing algorithms - these methods find an interval where at least one extrema of a continuous function exists

Acceleration bracketing - this method can be used with any continuous functions
Parabolic extrapolation bracketing - gives better results than acceleration bracketing for a large class of functions (functions that are locally parabolic about the extrema)
Acceleration bracketing for derivable functions - requires derivatives to be known; it's slower than the general acceleration algorithm but also safer

Locate algorithms - these methods converge to the extrema if the extrema is bracketed and the function under consideration is continuous

Parabolic interpolation locate - very fast algorithm but with moderate accuracy
Linear locate - slow algorithm but exhibits stable convergence
Brent locate - medium speed with good accuracy. With a good balance of speed and accuracy, this algorithm is very efficient to use
Cubic interpolation locate - very fast algorithm with reasonable accuracy; requires the derivatives to be known
Brent method for derivable functions - medium speed and good accuracy but requires derivatives to be known

Accurate `high level' algorithms - these algorithms are easy to use and offer high accuracy but are also very slow compared with the `low 'level' algorithms above (1,000 to 10,000 times slower). Use these algorithms when you need reliable results. The probability for a `high level' algorithm to make a mistake is much less than that of `low level' algorithms.

Method for continuous functions
Method for derivable functions

Global unidimensional optimization - finds global minima / maxima.

Methods for continuous functions
Methods for derivable functions

Unconstrained local multidimensional optimization

Methods for general functions - these algorithms do not require continuous functions

Downhill simplex method of Nelder and Mead - minimizes the function over a sequence of equal volume simplexes

Methods for continuous functions - these algorithms require the function to be continuous

Conjugate direction algorithms - this algorithm searches by iterating along conjugate paths

Powell's method - an implementation of the conjugate direction algorithm

Methods for derivable functions - these algorithms require the gradient of the function to be known

Steepest descent - a classical method with poor results, this method should mainly be used for testing purposes
Conjugate gradient algorithms - speed and accuracy highly dependent on the particular function, these methods can be deceived by `valleys' in the N-dimensional space

Fletcher-Reeves - an implementation of the conjugate gradient method
Polak-Riviere - an implementation of the conjugate gradient method

Variable metric algorithms/Quasi-Newton algorithms - slow speed; good results on a large class of continuous functions. The basic idea is to find the sequence of matrices which converges to the inverse Hessian of the function.

Fletcher-Powell - an implementation of the variable metric algorithm
Broyden-Fletcher-Goldfarb-Shanno - an implementation of the variable metric algorithm

Unconstrained global multidimensional optimization

Simulated annealing - a technique that has attracted significant attention as suitable for optimizing problems of large scale, especially ones where a desired global extremum is hidden among many poorer, local extrema

Constrained optimization for derivable functions with linear constraints

Rosen's gradient projection algorithm - uses the Kuhn-Tucker conditions as a termination criteria.

Linear programming - here the functions are linear and the constraints are linear

This product also contains the following feature:

GUI Bundle - we bundle a suite of graphical user interface JavaBean components allowing the developer to plug-in a wide range of GUI functionality (including charts/graphs) into their client applications.