Developing an Interior Point Method for Convex Quadratic Programming

Abstract

This thesis deal with the development of a primal-dual interior-point method for solving convex quadratic programming problems. The proposed approach is based on an algebraic transformation of the centrality condition in order to derive a new search direction that improves the efficiency and numerical performance of the algorithm. The theoretical properties of the method are investigated through convergence and computational complexity analyses. In addition, numerical experiments are conducted on a set of benchmark problems. The obtained results demonstrate that the proposed method efficiently reaches the optimal solution with a small number of iterations and satisfactory computational performance, confirming its effectiveness for solving convex quadratic programming problems.