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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:… (More)

- Che-Lin Su, Kenneth L. Judd, +20 authors Moshe Buchinsky
- 2007

Maximum likelihood estimation of structural models is often viewed as computationally difficult. This impression is due to a focus on the Nested FixedPoint approach. We present a direct optimization approach to the general problem and show that it is significantly faster than the NFXP approach when applied to the canonical Zurcher bus repair model. The NFXP… (More)

- Richard A. Waltz, José Luis Morales, Jorge Nocedal, Dominique Orban
- Math. Program.
- 2006

An interior-point method for nonlinear programming is presented. It enjoys the flexibility of switching between a line search method that computes steps by factoring the primal-dual equations and a trust region method that uses a conjugate gradient iteration. Steps computed by direct factorization are always tried first, but if they are deemed ineffective,… (More)

- Richard H. Byrd, Nicholas I. M. Gould, Jorge Nocedal, Richard A. Waltz
- Math. Program.
- 2004

This paper describes an active-set algorithm for large-scale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza [10]. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the active set at the solution. The linear program is obtained by… (More)

- Jorge Nocedal, Andreas Wächter, Richard A. Waltz
- SIAM Journal on Optimization
- 2009

This paper considers strategies for selecting the barrier parameter at every iteration of an interior-point method for nonlinear programming. Numerical experiments suggest that adaptive choices, such as Mehrotra’s probing procedure, outperform static strategies that hold the barrier parameter fixed until a barrier optimality test is satisfied. A new… (More)

- Richard H. Byrd, Jorge Nocedal, Richard A. Waltz
- Optimization Methods and Software
- 2008

This paper reviews, extends and analyzes a new class of penalty methods for nonlinear optimization. These methods adjust the penalty parameter dynamically; by controlling the degree of linear feasibility achieved at every iteration, they promote balanced progress toward optimality and feasibility. In contrast with classical approaches, the choice of the… (More)

- Richard H. Byrd, Nicholas I. M. Gould, Jorge Nocedal, Richard A. Waltz
- SIAM Journal on Optimization
- 2005

The global convergence properties of a class of penalty methods for nonlinear programming are analyzed. These methods include successive linear programming approaches, and more specifically, the successive linear-quadratic programming approach presented by Byrd, Gould, Nocedal and Waltz (Math. Programming 100(1):27–48, 2004). Every iteration requires the… (More)

- Richard H. Byrd, Jorge Nocedal, Richard A. Waltz
- Comp. Opt. and Appl.
- 2003

A slack-based feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust region methods, must be modified so that the feasible method is… (More)

This paper describes an active set algorithm for large scale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza The step computation is performed in two stages In the rst stage a linear program is solved to estimate the active set at the solution The linear program is obtained by making a linear… (More)

- Richard H. Byrd, Richard A. Waltz
- Optimization Methods and Software
- 2011

This paper describes an active-set algorithm for nonlinear programming that solves a parametric linear programming subproblem at each iteration to generate an estimate of the active set. A step is then computed by solving an equality constrained quadratic program based on this active-set estimate. This approach respresents an extension of the standard… (More)