Properties of two DC algorithms in quadratic programming

Authors:
Hoai An Le Thi;Tao Pham Dinh;Nguyen Dong Yen
Affiliations:
Laboratory of Theoretical and Applied Computer Science (LITA), Paul Verlaine university-Metz, Metz Cedex, France 57045;Laboratory of Modelling, Optimization and Operations Research (LMI), National Institute for Applied Sciences (INSA)-Rouen, Saint-Etienne-du-Rouvray Cedex, France 76801;Institute of Mathematics, Vietnamese Academy of Science and Technology, Hanoi, Vietnam 10307
Venue:
Journal of Global Optimization
Year:
2011

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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.