On the solution of linearly constrained optimization problems by means of barrier algorithms

Many practical problems require the solution of large-scale constrained optimization problems for which preserving feasibility is a key issue, and the evaluation of the objective function is very expensive. In these cases it is mandatory to start with a feasible approximation of the solution, the obtention of which should not require objective function evaluations. The necessity of solving this type of problems motivated us to revisit the classical barrier approach for nonlinear optimization, providing a careful implementation of a modern version of this method. This is the main objective of the present paper. For completeness, we provide global convergence results and comparative numerical experiments with one of the state-of-the-art interior-point solvers for continuous optimization.