Development of a corrector-predictor algorithm for convex quadratic optimization

Abstract

This manuscript introduces a new corrector-predictor interior-point algorithm for solving convex quadratic optimization problems. Inspired by the algebraic equivalent transformation technique, we define a modified transformed central path utilizing the specific function φ(t) = t - √t. This approach allows us to derive efficient Newton-type search directions for both the predictor and corrector steps. To demonstrate the practical efficiency and robustness of our proposed algorithm, a comprehensive numerical comparison is conducted against the standard primal-dual interior-point method and the recent weighted primal-dual interior-point algorithm (2024). The numerical results validate the computational superior performance of the proposed method