Global Optimization 3.0 for Mathematica

Global Optimization With Linear or Nonlinear Constraints.

PRODUCT DESCRIPTION

Global Optimization for Mathematica is a package designed to work with the Mathematica system.  It performs constrained and unconstrainednonlinear optimization, including global optimization.  Constraints an be nonlinear or linear.  It is designed to be very robust to localminima and nonsmooth functions.  No derivatives are required, andthe function can be discontinuous or black box.  It is able to findmultiple minima when they exist.
 

FUNCTIONALITY

Three functions are provided in release 2.0.

MultiStartMin -- This is a multistart, constrained hill-climbing algorithm. It automatically scales the search steps to avoid local minima.  Itfeatures a stochastic restart when a minimum is found to check if it is trapped in a local minimum.  It has been tested for many wavy andmulti-minimum functions (see below).  Problems with 100+ variablescan be run.

Examples of the types of problems that can be solved.

Extremely wavy function, solved successfully.

 Problem with nonlinear constraints, solution found is approximationto a circular solution space.

Problem with 6 solutions, all solutions found.

GlobalMinima -- This is a grid refinement algorithm, which is a step-wiseexhaustive search procedure.  This function is ideal for noisy problemswith less than 14 variables.  It is able to solve very noisy problems,including those shown above.  In addition, it has the unique featureof being able to give a rough definition of the optimal region, withinsome range of the best solution found.

MaxAllocation -- Allocation problems arise often in finance, when afixed amount of money can be invested in n options.  It also arisesin hedge fund creation.  For a nonlinear objective function, withpositivity and the single constraint that the sum of all xi must equalthe investment total, a path-following algorithm is able to solve the problemefficiently.  This means that problems with 300-1000 variables canbe solved on a workstation.

The function InterchangeMethod 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 type problems, even when the objective function is nonlinear. 

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