An explicit step length for solving an optimization problem

The problem of semi-definite programming (SDP) extends linear programming (LP) to solve a broader range of optimization problems, with significant advancements in algorithmic methods, particularly interior point techniques. In this article, we a logarithmic penalty approach for resolving SDP problems, where the direction of descent is determined using Newton's method. Additionally, for the step length, we propose new, more efficient, and robust lower bound functions. These proposed functions improve the accuracy and efficiency of the solution process. The effectiveness of the method is demonstrated through extensive numerical simulations, which validate the claims made in this study. The results confirm the practical feasibility and performance of the approach in solving complex semi-definite programming problems.