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, a trust region iteration that guarantees progress toward stationarity is invoked. To demonstrate its effectiveness, the algorithm is implemented in the Knitro [6,28] software package and is extensively tested on a wide selection of test problems.

We describe the most recent evolution of our constrained and unconstrained testing environment and its accompanying SIF decoder. Code-named SIFDecode and CUTEst, these updated versions feature dynamic memory allocation, a modern thread-safe Fortran modular design, a new Matlab interface and a revised installation procedure integrated with GALAHAD.

We describe the design of version 1.0 of GALAHAD, a library of Fortran 90 packages for large-scale nonlinear optimization. The library particularly addresses quadratic programming problems, containing both interior point and active set algorithms, as well as tools for preprocessing problems prior to solution. It also contains an updated version of the venerable nonlinear programming package, LANCELOT.

Interior-point methods in augmented form for linear and convex quadratic programming require the solution of a sequence of symmetric indefinite linear systems which are used to derive search directions. Safeguards are typically required in order to handle free variables or rank-deficient Jacobians. We propose a consistent framework and accompanying theoretical justification for regularizing these linear systems. Our approach can be interpreted as a simultaneous proximal-point regularization of the primal and dual problems. The regularization is termed exact to emphasize that, although the problems are regularized, the algorithm recovers a solution of the original problem, for appropriate values of the regularization parameters. Mathematics Subject Classification (2000)90C05 · 90C06 · 90C20 · 90C25 · 90C51 · 65F22 · 65F50