Document Type : Research Paper

Authors

• Negin Bagherpour ¹
• Nima Minayi ²
• Amirhossein Shanaghi ³

¹ Department of Engineering Sciences, University of Tehran

² Department of Engineering Sciences, University of Tehran, Tehran, Iran

³ Department of Engineering Sciences, University of Tehran, Tehran, Iran.

Abstract

Convex quadratic programming (QP) arises in many applications such as control theory, economics, and robotics. In this paper, we propose two active-set schemes for solving convex QP problems by exploiting structural properties of the Karush–Kuhn–Tucker (KKT) system. The proposed methods are implemented and tested on randomly generated problems as well as benchmark instances from the CUTEst test collection. In total, 2000 numerical experiments are conducted to evaluate the performance of the algorithms. The numerical results indicate that the proposed approaches reduce computational time compared with the classical active-set method, with the first strategy performing better for problems with few constraints and the second showing improved efficiency when the number of independent constraints is large.

Keywords

• Quadratic programming
• Active Set
• SVD
• Spectral Decomposition
• KKT