An Interior Point Algorithm for Quadratic Programming Based on a New Step-Length

Résumé

Interior point methods have seen significant advancements in recent decades for solving linear, semi-definite and quadratic programming. Among these methods, the logarithmic barrier methods based on approximate functions have polynomial convergence and are known for their favorable numerical performance. In this work, a new minorant function for the barrier method is proposed for solving convex quadratic problems with inequality constraints. The proposed minorant function allows to compute the steplength easily and quickly, unlike the line search method, which is computationally intensive and time-consuming. Mathematical results concerning the convergence of the algorithm are established. The numerical comparisons with the inexact Wolfe line search technique show that the proposed method is promising and effective.

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