On implementing a primal-dual interior-point method for conic quadratic optimization

Conic quadratic optimization is the problem of minimizing a linear function subject to the intersection of an affine set and the product of quadratic cones. The problem is a convex optimization problem and has numerous applications in engineering, economics, and other areas of science. Indeed, linear and convex quadratic optimization is a special case. Conic quadratic optimization problems can in theory be solved efficiently using interior-point methods. In particular it has been shown by Nesterov and Todd that primal-dual interior-point methods developed for linear optimization can be generalized to the conic quadratic case while maintaining their efficiency. Therefore, based on the work of Nesterov and Todd, we discuss an implementation of a primal-dual interior-point method for solution of large-scale sparse conic quadratic optimization problems. The main features of the implementation are it is based on a homogeneous and self-dual model, handles the rotated quadratic cone directly, employs a Mehrotra type predictor-corrector ∗Helsinki School of Economics and Business Administration, Department of Economics and Management Science, Runeberginkatu 14-16, Box 1210, FIN-00101 Helsinki, Finland, Email: [email protected]. Part of this research was done while the author had a TMR fellowship at TU Delft. This author has been supported by the Finnish Academy of Science †TU Delft, Mekelweg 4, 2628 CD Delft, The Netherlands, Email: [email protected]. ‡McMaster University, Department of Computing and Software, Hamilton, Ontario, Canada. L8S 4L7. Email: [email protected]. Part of this research was done while the author was employed at TU Delft.