abstract 95

Bulletin of Computational Applied Mathematics (Bull CompAMa) 

95

A primal-dual interior point method for high precision solutions of quadratic programming (Research Paper)

María D. Gonzalez-Lima, Aurelio R.L. Oliveira, Danilo E. Oliveira.

In this paper we present a primal-dual interior point method for solving convex quadratic programming problems (QP) in standard form. The method is based on the Stable system presented by Gonzalez-Lima et al [1] (gonzalezlima2009). The main feature of the method is that the linear system solved at each iteration does not introduce inverse of variables that are zero at the solution, as in standard approaches. As a consequence highly accurate solutions of the optimization problem can be found. We compare the proposed method with Quadprog, the Matlab primal-dual interior-point code for solving QP. Our numerical experimentation shows that the proposed method is able to solve more instances of the optimization problems when small tolerances are required. Furthermore, the number of iterations required for convergence is many times less than the ones needed by the optimized Quadprog.

Keywords: Quadratic programming; primal-dual interior point methods; stable system.

Cite this paper:

Gonzalez-Lima M.D., Oliveira A.R.L., Oliveira D.E.

A primal-dual interior point method for high precision solutions of quadratic programming

Bull. Comput. Appl. Math. (Bull CompAMa)

Vol. 12, No.1 pp.161-193, 2024.