WebCab Optimization for .NET
Refined procedures for solving and performing sensitivity analysis on uni and multi dimensional, local or global
optimization problems which may or may not have linear constraints. Specialized Linear programming algorithms based on the
Simplex Algorithm and duality are included along with a framework for sensitivity analysis w.r.t. boundaries (duality, or
direct approach), or object function coefficients.
- Windows 9x/NT/2000/XP/2003
- Pentium II® 500Mhz
- .NET Framework v1.x
|Full version: 4.19 MB
|Free to try, $ 179 to buy
This suite includes the following features:
- Local unidimensional optimization - finds
global minima / maxima for continuous functions in one dimension
- 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
- 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
- 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
- Simplex algorithm - Kuenzi, Tszchach and Zehnder implementation of the simplex algorithm
for linear programming
- Duality - Construct and solve the dual problem for a given primal linear programming problem.
- Sensitivity Analysis - Study how the location and value of the extremum varies under
perturbations of the object function and parallel shifts of the linear constraints. Sensitivity analysis of the boundaries
can very efficient be carried out with the application a duality techniques.
- Sensitivity Analysis - Stability of the value and location of the extremum
- General Framework - Perform sensitivity analysis on any optimization problem/algorithm combination.
- Flexibility - Perform sensitivity analysis on the object function, constraints and/or algorithm.
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