A numerical study of an infeasible interior-point algorithm for convex quadratic semi-definite optimization

• Published in: Journal of Numerical Analysis and Approximation Theory
• Main Authors: Yasmina Bendaas, Mohamed Achache
• Format: Article
• Language: English
• Published: Publishing House of the Romanian Academy 2024-12-01
• Subjects: Convex quadratic semidefinite optimization, Interior-point methods, Primal-dual algorithm, Newton method.
• Online Access: https://ictp.acad.ro/jnaat/journal/article/view/1442
• ISSN: 2457-6794; 2501-059X

The focus of this research is to apply primal-dual interior-point pathfollowing methods, specifically those derived from Newton’s method for solving convex quadratic semidefinite optimization (CQSDO) problems. In this paper, we present a numerical study of an infeasible primal-dual interior-point method for tackling this class of optimization problems. Unlike the feasible interior-point algorithms, the proposed algorithm can be start with any initial positive definite matrix and does not require the strictly feasible initial points. Under certain conditions, the Newton system is well defined and its Jacobian is nonsingular at the solution. For computing an iteration throughout the algorithm, a Newton direction and a step-size are determined. Here, our search direction is based on Alizadeh-Haeberly-Overton (AHO) symmetrization. However, for the step size along this direction an efficient procedure is suggested. Preliminary numerical results demonstrate the efficiency of our algorithm.