Features

New in KNITRO 6 for Mathematica

• Solving optimization models (both linear and nonlinear) with binary or integer variables
• Two algorithms for mixed-integer nonlinear programming (MINLP). The first is a nonlinear branch and bound method and the second implements the hybrid Quesada–Grossman method for convex MINLP. The MINLP code is designed for convex mixed-integer programming and is a heuristic for nonconvex problems.
• Mixed-integer programming (MIP)
• The MIP code also handles mixed-integer linear programs (MILP) of moderate size
• Special user options to allow user control over the MIP methods
• Improved multi-start generation of new start points and new user option "ms_maxbndrange"

General Features

• Solves large-scale general nonlinear programming (NLP) problems (continuous, binary, or integer variables; smooth functions)
• Particular convex mixed-integer nonlinear problems (MINLP)
• Solves large-scale linear programming (LP) problems
• Solves large-scale quadratic programming (QP) problems, both convex and nonconvex
• Solves large-scale nonlinear least squares problems, and nonlinear systems of equations
• Provides two state-of-the-art optimizer algorithms: interior-point (barrier) and active-set
• Solves small or large optimization problems efficiently and robustly:
  • Rapidly converges to a high-precision local solution using Newton-based methods
  • Computes analytic derivatives from Mathematica's symbolic problem definition
  • Linear algebra operations choose between iterative (conjugate gradient) and direct (sparse factorization) methods
• Provides special options for difficult or unusual problems:
  • Can require that every iterate remains feasible with respect to all inequality constraints
  • Can cross over from the interior-point algorithm to the active-set one for final determination of a vertex solution
• Offers several choices for high-precision Newton-based solution methods:
  • Solve with Mathematica's analytic second derivatives
  • Solve with finite difference approximation of second derivatives
  • Solve with dense quasi-Newton approximations (BFGS and SR1)
  • Solve with limited-memory quasi-Newton approximation (L-BFGS)
  • Select your own starting point or let KNITRO for Mathematica compute one for you