Year: 2024
Type: preprint
Abstract: Two inertial DC algorithms for indefinite quadratic programs under linear constraints (IQPs) are considered in this paper. Using a qualification condition related to the normal cones of unbounded pseudo-faces of the polyhedral convex constraint set, the recession cones of the corresponding faces, and the quadratic form describing the objective function, we prove that the iteration sequences in question are bounded if the given IQP has a finite optimal value. Any cluster point of such a sequence is a KKT point. The convergence of the members of a DCA sequence produced by one of the two inertial algorithms to just one connected component of the KKT point set is also obtained. To do so, we revisit the inertial algorithm for DC programming of de Oliveira and Tcheou [de Oliveira, W., Tcheou, M.P.: An inertial algorithm for DC programming, Set-Valued and Variational Analysis 2019; 27: 895--919] and give a refined version of Theorem 1 from that paper, which can be used for IQPs with unbounded constraint sets. An illustrative example is proposed.
Source: arXiv (Cornell University)
Authors: Cuong, Tran Hung, Lim, Yongdo, Thieu, Nguyen Nang, Yen, Nguyen Dong
Institutions: Hanoi University of Industry, Sungkyunkwan University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4393931088