Unleashing Knitro’s Power through AMPL Integration
Artelys Knitro is an especially powerful nonlinear solver, offering a range of state-of-the-art algorithms and options for working with smooth objective and constraint functions in continuous and integer variables. It is designed for local optimization of large-scale problems with up to hundreds of thousands of variables.
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Artelys Knitro is distinguished as a leading nonlinear solver, celebrated for its robust and efficient algorithms. Initially developed by Ziena Optimization in the early 2000s and subsequently acquired by Artelys, Knitro boasts a legacy of continuous innovation. It excels in handling large-scale nonlinear problems, making it the go-to solution in industries such as finance, energy management, and engineering design, where near-optimal solutions must be achieved swiftly and effectively.
Knitro is renowned for its proficiency in addressing a diverse range of optimization challenges, from straightforward continuous unconstrained problems to the more complex mixed-integer nonlinear programs (MINLPs). Its forte lies in efficiently solving large-scale, smooth convex nonlinear optimization problems, but its capabilities extend to non-convex quadratic programming (QPs) and finding local solutions of general nonlinear programs (NLPs) as well.
Knitro’s integration with AMPL through a user-friendly interface enhances its accessibility, making it an intuitive yet potent tool for professionals and researchers striving to solve demanding optimization problems with efficiency.
Unconstrained, bound constrained, systems of nonlinear equations, linear and nonlinear least squares problems, linear programming problems (LPs), convex and non-convex quadratic programming problems (QPs), quadratically constrained quadratic programs (QCQPs), second order cone programs (SOCPs), mathematical programs with complementarity constraints (MPCCs), both convex and non-convex general nonlinear (smooth) constrained problems (NLP), mixed integer linear programs (MILP) of moderate size, mixed integer (convex) nonlinear programs (MINLP) of moderate size, derivative free (DFO) or black-box optimization.
Complementarity and equilibrium constraints using the AMPL “complements” operator.
At its core, Knitro is powered by four sophisticated optimization algorithms: the direct and conjugate-gradient interior point methods, the active set method, and the sequential quadratic programming method. Mixed-integer nonlinear programs are solved using either a non-linear branch-and-bound (NLPBB) algorithm or mixed-integer sequential quadratic programming (MISQP) algorithm. The MISQP method is designed for problems with expensive function evaluations and can handle non-relaxable integer variables.
Extensive use of shared-memory multi-core computing: concurrent optimization to determine the best choice among multiple algorithms; a parallel multi-start procedure for non-convex problems to prevent users from settling on the initial locally optimal solution encountered; parallel linear algebra and finite-difference gradient computations. Options to keep iterates feasible with respect to bounds and inequalities. Special handling of quadratic objectives and constraints to improve efficiency.