Knitro: An Integrated Package for Nonlinear Optimization

Abstract

This paper describes Knitro 5.0, a C-package for nonlinear optimization that combines complementary approaches to nonlinear optimization to achieve robust performance over a wide range of application requirements. The package is designed for solving large-scale, smooth nonlinear programming problems, and it is also effective for the following special cases: unconstrained optimization, nonlinear systems of equations, least squares, and linear and quadratic programming. Various algorithmic options are available, including two interior methods and an active-set method. The package provides crossover techniques between algorithmic options as well as automatic selection of options and settings.

A mixed-binary non-linear programming approach for the numerical solution of a family of singular optimal control problems

“…We have implemented the method using Matlab in a personal computer and to solve the final BINLP (32), the solver Knitro (Byrd, Nocedal, & Waltz, 2006) has been interfaced and function knitromatlab mip is used. We test the feasibility and validity of the presented method on four optimal control problems.…”

Computational optimization of gas compressor stations: MINLP models versus continuous reformulations

“…As global solvers for the MINLP model and its continuous (NLP type) reformulations we use BARON 12.3.3 (Tawarmalani and Sahinidis 2002 and SCIP 3.0 (SCIP 2015;Vigerske 2012). Additionally, we use the convex MINLP solver KNITRO 8.1.1 (Byrd et al 2006) as a heuristic for the nonconvex MINLPs and as NLP solver for the continuous reformulations. As local solvers for the continuous reformulations we use the interior-point code Ipopt 3.11 (Wächter and Biegler 2006) and the reduced-gradient code CONOPT4 (Drud 1994(Drud , 1995(Drud , 1996 as well as the three MINLP solvers.…”

On mutual impact of numerical linear algebra and large-scale optimization with focus on interior point methods

“…Direct methods are widely used for solving the KKT systems in well-established optimization codes based on IP methods, such as MOSEK [61], LOQO [77,78], OOQP [37], KNITRO-Interior/Direct [12], IPOPT [79]. In this case, modified Cholesky factorizations [19,40,72], that are capable of handling the case the matrix is not positive definite, are usually applied to the condensed system, while LBL T factorizations, where L is unit lower triangular and B is symmetric block diagonal with 1 × 1 or 2 × 2 blocks, are applied to the KKT system.…”

“…This has motivated in the last years an increasing research activity devoted to the development of suitable iterative techniques for solving the KKT systems. Examples of optimization codes implementing such techniques are available, such as KNITROInterior/CG [12], HOPDM [44] and PRQP (see Section 5). Due to the ill conditioning of the KKT system, effective preconditioners must be used to obtain useful search directions.…”