On a solution method in indefinite quadratic programming under linear constraints

Abstract

We establish some properties of the Proximal Difference-of-Convex functions decomposition algorithm in indefinite quadratic programming under linear constraints. The first property states that any iterative sequence generated by the algorithm is root linearly convergent to a Karush–Kuhn–Tucker point, provided that the problem has a solution. The second property says that iterative sequences generated by the algorithm converge to a locally unique solution of the problem if the initial points are taken from a suitably chosen neighbourhood of it. Through a series of numerical tests, we analyse the influence of the decomposition parameter on the rate of convergence of the iterative sequences and compare the performance of the Proximal Difference-of-Convex functions decomposition algorithm with that of the Projection Difference-of-Convex functions decomposition algorithm. In addition, the performances of the above algorithms and the Gurobi software in solving some randomly generated nonconvex quadratic programs are compared.

Keywords:

• Quadratic programming
• KKT point
• DCA sequence
• linear convergence
• asymptotic stability

Acknowledgments

Helpful and insightful comments of the two anonymous referees, the handling Associate Editor, and Dr. Le Xuan Thanh are gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author was supported by Hanoi University of Industry under project number 24-2022-RD-HD-DHCN. The second and third authors were supported, respectively, by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) No. 2015R1A3A2031159 and Vietnam Academy of Science and Technology. The first and third authors would like to thank the Sungkyunkwan University for supporting their research stays in Suwon.