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Knitro for Mathematica

KNITRO for Mathematica stellt Mathematica die führende Software für nichtlineare Optimierung zur Verfügung. Dieses Anwendungspaket berechnet ein lokales Minimum bei allgemeinen Optimierungsproblemen, die Mathematica Funktionen und Objekte benutzen. Jedes Optimierungsproblem mit stetigen Variablen und glatten Funktionen kann gelöst werden. Das Paket benutzt eingebaute Mathematica Funktionen, um dünn besetzte Matrizen für die ersten und zweiten Ableitungen zu konstruieren und auszuwerten.

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.

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

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