On a solution method in indefinite quadratic programming under linear constraints

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.

Automated summary

This study investigates the properties of the Proximal Difference-of-Convex functions decomposition algorithm in indefinite quadratic programming with linear constraints. It is found that the algorithm can converge to a Karush-Kuhn-Tucker point at a root linear rate, provided that the problem has a solution. Moreover, when the initial points are chosen from a suitable neighborhood, the algorithm can converge to a locally unique solution. Through numerical tests, the influence of the decomposition parameter on the convergence rate is analyzed, and the performance of the Proximal Difference-of-Convex functions decomposition algorithm is compared with that of the Projection Difference-of-Convex functions decomposition algorithm. Additionally, the performances of these algorithms and the Gurobi software are compared in solving randomly generated nonconvex quadratic programs.