Knitro: An Integrated Package for Nonlinear Optimization

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.

[1]  Boris Polyak The conjugate gradient method in extremal problems , 1969 .

[2]  Michael A. Saunders,et al.  MINOS 5. 0 user's guide , 1983 .

[3]  Gene H. Golub,et al.  Matrix computations , 1983 .

[4]  Arne Drud,et al.  CONOPT: A GRG code for large sparse dynamic nonlinear optimization problems , 1985, Math. Program..

[5]  Roger Fletcher,et al.  Nonlinear programming and nonsmooth optimization by successive linear programming , 1989, Math. Program..

[6]  N. Megiddo Pathways to the optimal set in linear programming , 1989 .

[7]  P. Toint,et al.  Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A) , 1992 .

[8]  Jan Vlcek,et al.  Indefinitely preconditioned inexact Newton method for large sparse equality constrained non-linear programming problems , 1998, Numer. Linear Algebra Appl..

[9]  L. Luksan,et al.  Indefinitely preconditioned inexact Newton method for large sparse equality constrained non‐linear programming problems , 1998 .

[10]  Sven Leyffer,et al.  User manual for filterSQP , 1998 .

[11]  Robert J. Vanderbei,et al.  An Interior-Point Algorithm for Nonconvex Nonlinear Programming , 1999, Comput. Optim. Appl..

[12]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[13]  Jorge Nocedal,et al.  An Interior Point Algorithm for Large-Scale Nonlinear Programming , 1999, SIAM J. Optim..

[14]  Jorge Nocedal,et al.  A trust region method based on interior point techniques for nonlinear programming , 2000, Math. Program..

[15]  Lorenz T. Biegler,et al.  Failure of global convergence for a class of interior point methods for nonlinear programming , 2000, Math. Program..

[16]  Nicholas I. M. Gould,et al.  Constraint Preconditioning for Indefinite Linear Systems , 2000, SIAM J. Matrix Anal. Appl..

[17]  Knud D. Andersen,et al.  The Mosek Interior Point Optimizer for Linear Programming: An Implementation of the Homogeneous Algorithm , 2000 .

[18]  Nicholas I. M. Gould,et al.  Trust Region Methods , 2000, MOS-SIAM Series on Optimization.

[19]  Nicholas I. M. Gould,et al.  On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization , 2001, SIAM J. Sci. Comput..

[20]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2002, SIAM J. Optim..

[21]  Christian Prins,et al.  Applications of optimisation with Xpress-MP , 2002 .

[22]  Jorge Nocedal,et al.  Assessing the Potential of Interior Methods for Nonlinear Optimization , 2003 .

[23]  M. Heinkenschloss,et al.  Large-Scale PDE-Constrained Optimization , 2003 .

[24]  Roger Fletcher,et al.  On the global convergence of an SLP–filter algorithm that takes EQP steps , 2003, Math. Program..

[25]  Jorge Nocedal,et al.  Feasible Interior Methods Using Slacks for Nonlinear Optimization , 2003, Comput. Optim. Appl..

[26]  Jorge Nocedal,et al.  A starting point strategy for nonlinear interior methods , 2004, Appl. Math. Lett..

[27]  Jorge Nocedal,et al.  On the convergence of Newton iterations to non-stationary points , 2004, Math. Program..

[28]  Nicholas I. M. Gould,et al.  An algorithm for nonlinear optimization using linear programming and equality constrained subproblems , 2004, Math. Program..

[29]  G. M. Ostrovsky,et al.  Linearly constrained optimization , 1989, Computing.

[30]  Nicholas I. M. Gould,et al.  On the Convergence of Successive Linear-Quadratic Programming Algorithms , 2005, SIAM J. Optim..

[31]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[32]  Todd S. Munson,et al.  Optimality Measures for Performance Profiles , 2006, SIAM J. Optim..

[33]  Jorge Nocedal,et al.  An interior algorithm for nonlinear optimization that combines line search and trust region steps , 2006, Math. Program..

[34]  J. Nocedal,et al.  Adaptive Barrier Strategies for Nonlinear Interior Methods , 2022 .