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Global Optimization 5.1 for Mathematica
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Global Optimization 5.1 for Mathematica is a collection of functions for constrained and unconstrained global nonlinear optimization. The tools in this package are able to solve some of the most challenging optimization problems. It has been tested against the built-in Mathematica functions and against 3rd party packages, as well as against Matlab toolboxes, and solves many problems these other products fail to solve, including 10,000 variable problems. It uses the Mathematica system as an interface for defining the nonlinear system to be solved and for computing function numeric values. Any function computable by Mathematica can be used as input, including degree of fit of a model against data, black-box functions, and simulation models. In use since early 1998, the package is well tested by a worldwide community of users.
Ten functions are provided in the package.
· The function GlobalSearch is a hill-climbing algorithm for nonlinear functions with analytic equality and inequality constraints. It is designed to be robust to local minima and to solve problems with hundreds of variables. No derivatives are required, and the user objective function can even be nondifferentiable. Multiple starts allow the user to find multiple minima if they exist. This function is ideal for nonlinear regression, engineering design, model estimation, financial analysis, and other applications. Bounds are not required, nor is a close initial guess needed.
· The function GlobalPenaltyFn is a hill-climbing algorithm for nonlinear functions with nonanalytic equality and inequality constraints. It is designed to be robust to local minima and to solve problems with hundreds of variables. No derivatives are required, and the user objective function can even be nondifferentiable. Multiple starts allow the user to find multiple minima if they exist. Bounds are not required, nor is a close initial guess needed.
· The function IntervalMin solves problems using interval methods. It is designed to be robust to local minima, and the problems can have inequality constraints. No derivatives are required, and the user objective function can even be nondifferentiable. This function is ideal for nonlinear regression, engineering design, model estimation, financial analysis, and other applications.
· The function MultiStartMin is a hill-climbing algorithm for constrained (including bound constrained) and unconstrained nonlinear functions. It is designed to be robust to local minima and to solve midsized problems (up to 15 variables). No derivatives are required, and the user objective function can even be nondifferentiable. Multiple starts allow the user to find multiple minima if they exist. Variables can be any mix of continuous, integer, and discrete. The integer feature allows knapsack and similar problems to be solved. This function is ideal for nonlinear regression, engineering design, model estimation, financial analysis, and other applications. Bounds are not required, nor is a close initial guess needed.
· The function NLRegression solves nonlinear regression problems. A sensitivity analysis of parameter values around the solution point is provided. Confidence intervals are computed. Both L1 and L2 norms can be used. Constrained regression problems can also be solved.
· The function MaxLikelihood solves maximum likelihood estimation problems. Summary statistics are provided. Problems can be constrained to obtain better solutions. A library of common univariate functions that are optimized for speed is provided.
· The function InterchangeMethodMin is a function for 0-1 integer problems with a linear or nonlinear objective function. It can solve routing, traveling salesman, minimal spanning tree, and other discrete network problems even when the objective function is nonlinear.
· The function TabuSearchMin is a function for 0-1 integer problems with a linear or nonlinear objective function and is related to the interchange method approach described above. The tabu feature increases efficiency on complex problems. It can solve routing, traveling salesman, minimal spanning tree, and other discrete network problems even when the objective function is nonlinear.
· The function GlobalMinima solves smaller constrained or unconstrained global nonlinear models. This algorithm is based on the identification of feasible points that define the solution set at each iteration. As lower points are found during the grid refinement process, points far from the current optimum are pruned from the solution set. As a result, multiple minima, if they exist, can be found in a single run. The algorithm can also identify optimal regions rather than only single points. These optimal regions might represent the bounds on feasible management strategies that achieve an equivalent result, or they might depict confidence limits for a parameter estimation problem.
· The function MaxAllocation is designed for allocation problems such as arise in investment, where a fixed amount of money is to be allocated across a series of investment options. Such problems have a single equality constraint and a positivity restriction on all variables. The path-following algorithm used is able to solve this type of problem with high efficiency, leading to the solution of problems with many hundreds to over one thousand variables. This function is ideal for quadratic programming, investment allocation, and hedge fund creation applications.
Developed and supported by Loehle Enterprises. Registered users receive free updates.
Global Optimization 4.3 requires Mathematica 3 or later and is available for all Windows platforms (95 and later), Macintosh, Linux, and all Unix platforms. Price: $395 USD.
| Global Optimization for C++
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Global Optimization for C++ is an algorithm for constrained and unconstrained global nonlinear optimization. The function is a C++ translation of the popular Global Optimization for Mathematica general nonlinear solver. It has been tested against the built-in Mathematica functions and against 3rd party packages, as well as against Matlab toolboxes, and solves problems these other products fail to solve. The solver comes as a dll, with public subroutines for user definition of equations and constraints. Program written in ANSI C++ for complete portability. It may be linked into Matlab codes.
A discrete gradient hill-climbing algorithm is used for nonlinear functions with analytic or nonanalytic equality and/or inequality constraints. A unique approach is used to handle constraints, with equality constraints solved exactly. It is designed to be robust to local minima and to solve problems with hundreds of variables. No derivatives are required, and the user objective function can even be nondifferentiable or discontinuous. Multiple starts allow the user to find multiple minima if they exist. Bounds are not required, nor is a close initial guess needed. The algorithm is extremely robust and fast.
The algorithm has been tested on many difficult problems such as the Rosenbrock, Hyper-ellipsoid, Neumaier, Goldstein-Price, Branin, camel-back, the Lennard-Jones atom packing problem, and other functions with excellent results. It finds solutions to problems where other methods such as Simulated Annealing, Genetic Algorithm, SQP, and other methods fail. It is able to solve problems with hundreds of variables. Applications include nonlinear regression, operations research, optimal control, finance, options trading, engineering design, curve fitting, economics, and mathematics.
Developed and supported by Loehle Enterprises. Academic price $400 USD. Commercial price call for info.
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Our experts can help you solve optimization problems in operations research, engineering, finance, and other fields. From problem definition to numerical solution, we have the expertise you need.
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Course and book (http://www.amazon.com/exec/obidos/tg/detail/-/0521568412/qid=1050421728/sr=1-4/ref=sr_1_4/103-3229382-4226241?v=glance&s=books) offered on professional productivity.
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