A new kernel function and iteration bounds for convex quadratic programming

Abstract

This thesis focuses on the study and development of primal-dual interior-point methods (IPMs) applied to convex quadratic programming (CQP) problems. The objective of this work is to integrate and analyze a new kernel function to efficiently solve convex quadratic programs. We present a detailed algorithmic study then establish the theoretical polynomial complexity for large-step methods, which turns out to be identical to that of small-step methods (namely O(√n log( 𝑛/𝜀))), Finally, to evaluate the performance of our algorithm, numerical tests and a comparative study have been carried out on a varied series of examples.