On a solution method in indefinite quadratic programming under linear constraints

• Published in: Optimization Vol. 73; no. 4; pp. 1087 - 1112
• Main Authors: Cuong, Tran Hung, Lim, Yongdo, Yen, Nguyen Dong
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.04.2024; Taylor & Francis LLC
• Subjects: Algorithms; asymptotic stability; Convergence; DCA sequence; Decomposition; Iterative methods; KKT point; linear convergence; Quadratic programming; Sequences
• ISSN: 0233-1934; 1029-4945
• DOI: 10.1080/02331934.2022.2141056

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.