An Infeasible Interior-point Arc-search Algorithm for Nonlinear Constrained Optimization

TL;DR

This paper introduces an infeasible arc-search interior-point algorithm for nonlinear programming that uses an arc approximation instead of a straight line, showing improved iteration efficiency in benchmark tests.

Contribution

It presents a novel arc-search interior-point method for nonlinear optimization, with convergence analysis and enhanced variants for faster performance.

Findings

Fewer iterations to reach optimality compared to line-search methods.

Longer total computation time despite fewer iterations.

Modified arc-search algorithm achieves faster convergence.

Abstract

In this paper, we propose an infeasible arc-search interior-point algorithm for solving nonlinear programming problems. Most algorithms based on interior-point methods are categorized as line search, since they compute a next iterate on a straight line determined by a search direction which approximates the central path.The proposed arc-search interior-point algorithm uses an arc for the approximation.We discuss convergence properties of the proposed algorithm.We also conduct numerical experiments on the CUTEst benchmark problems and compare the performance of the proposed arc-search algorithm with that of a line-search algorithm. Numerical results indicate that the proposed arc-search algorithm reaches the optimal solution using less iterations but longer time than a line-search algorithm. A modification that leads to a faster arc-search algorithm is also discussed.