Analysis and numerical estimation of the step size in optimization problems

Abstract

Several studies have focused on determining the optimal step size for a wide range of optimization problems. {In the present study,} we propose  {a novel} minorant function within {the barrier approach} framework {to address} convex quadratic problems with inequality constraints. The paper presents a comparative numerical analysis between traditional line search methods and the proposed minorant function for step-size determination in the logarithmic barrier method. {The findings of our numerical experiments indicate that} minorant function outperforms line search methods, making it a more effective and reliable approach.