KNITRO for Mathematica 5.1

A Solver for Large-Scale Nonlinear Optimization

KNITRO for Mathematica brings the leading software tool for large-scale nonlinear optimization to Mathematica. This application package computes a local minimum to general optimization problems composed from Mathematica functions and objects. Any optimization problem with continuous variables and smooth functions can be solved. The package uses built-in Mathematica functionality to construct and evaluate sparse first and second derivatives.

KNITRO for Mathematica is an industrial-strength solver for large-scale nonlinear optimization, and readily handles complex real-world problems. It solves the following problem types, for small or large numbers of unknowns and constraints:

• General constrained (inequalities)
• Unconstrained
• Bound constrained
• Equality constrained, both linear and nonlinear
• Systems of nonlinear equations
• Least squares, both linear and nonlinear
• Linear programming (LP)
• Quadratic programming (QP), both convex and nonconvex

KNITRO for Mathematica offers two state-of-the-art algorithms, active-set and interior-point, each employing sparse linear algebra techniques for maximum efficiency on large problems.

Other KNITRO for Mathematica features include:

• Several choices among Newton-based methods that rapidly converge to a high-precision local solution
• Analytic second derivatives
• Finite difference approximation of second derivatives
• Dense quasi-Newton approximations (BFGS and SR1)
• Limited-memory quasi-Newton approximation (L-BFGS)
• An option requiring that every iterate remains feasible with respect to all inequality constraints and variable bounds
• An option to cross over from the interior-point algorithm to the active-set one for final determination of a vertex solution
• Linear algebra operations that choose between iterative (conjugate gradient) and direct (sparse factorization) methods
• Automatic selection of the starting point

KNITRO for Mathematica is a local solver, which means that for nonlinear problems with multiple local minima, it will converge to any one of the local minima. Users can specify different starting points to try to locate the best local minimum. KNITRO for Mathematica also requires variables to be continuous; for example, it cannot restrict a variable to take only integer values.

About the Developers

Ziena Optimization's founders include a world-renowned team of scientists specializing in nonlinear and large-scale optimization. Their areas of expertise encompass modeling and solving of optimization problems arising in business and engineering. The methods and software created by Ziena's scientists are in use at hundreds of sites worldwide to address a variety of problems in energy, communications, finance, and engineering.

Product Support

KNITRO for Mathematica is developed and supported by Ziena Optimization, Inc.

KNITRO for Mathematica 5.1 requires Mathematica 6 and is available for Windows and Linux. For versions for Sun Solaris and some Linux x86(64-bit) platforms, please contact the developer.

KNITRO is © 2001-2007 Ziena Optimization, Inc.

Note: Contact the developer for upgrade or trial information.