Le Thi Hoai An, Pham Dinh Tao, Nguyen Dong Yen: "Properties of two DC algorithms in quadratic programming".

Abstract: Some new properties of the Projection DC decomposition algorithm (we call it Algorithm A) and the Proximal DC decomposition algorithm (we call it Algorithm B) Pham Dinh et al. in Optim Methods Softw, 23(4): 609–629 (2008) for solving the indefinite quadratic programming problem under linear constraints are proved in this paper. Among other things, we show that DCA sequences generated by Algorithm A converge to a locally unique solution if the initial points are taken from a neighborhood of it, and DCA sequences generated by either Algorithm A or Algorithm B are all bounded if a condition guaranteeing the solution existence of the given problem is satisfied.

 
Keywords: Quadratic programming, DC algorithm, KKT point, Local solution, DCA sequence, Convergence, Boundedness.
 
Citation: Le Thi Hoai An, Pham Dinh Tao, Nguyen Dong Yen, Properties of two DC algorithms in quadratic programming, Journal of Global Optimization, Volume 49, Number 3, pp. 481-495, 2011.