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

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Abstract. We compare six state-of-the-art local optimization solvers with focus on their efficiency when invoked within an interval-based global optimization algorithm. For comparison purposes we design three special performance indicators: a solution check indicator (measuring whether the local minimizers found are good candidates for near-optimal verified feasible points), a function value indicator (measuring the contribution to the progress of the global search), and the running time indicator (estimating the computational cost of the local search within the global search). The solvers are compared on the COCONUT Environment test set consisting of 1307 problems. Our main target is to predict the behavior of the solvers in terms of the three performance indicators on a new problem. For this we introduce a k-nearest neighbor method applied over a feature space consisting of several categorical and numerical features of the optimization problems. The quality and robustness of the prediction is demonstrated by various quality measurements with detailed comparative tests. In particular, we found that on the test set we are able to pick a ‘best ’ solver in 66–89 % of the cases and avoid picking all ‘useless ’ solvers in 95–99 % of the cases (when a useful alternative exists). The resulting automated solver selection method is implemented as an inference engine of the COCONUT Environment.

We propose a new globalization strategy for primal-dual interior-point methods in nonlinear programming that relaxes the requirement of closely following the central path and lends itself to dynamic updates of the barrier parameter. The latter promote better synchonization between the barrier parameter and the optimality residual, and increase robustness. Global convergence is proved under mild assumptions. We show that the unit Newton step is asymptotically accepted and that linear or superlinear convergence occurs when the barrier parameter goes to zero linearly or superlinearly. Numerical experiments illustrate our results.

Abstract. Ipopt is an open-source software package for large-scale nonlinear optimization. This tutorial gives a short introduction that should allow the reader to install and test the package on a UNIX-like system, and to run simple examples in a short period of time. Keywords. Nonlinear Optimization, Tutorial, Ipopt, COIN-OR 1