Boundedness of a Type of Iterative Sequences in Two-Dimensional Quadratic Programming

Linear convergence of a type of iterative sequences in nonconvex quadratic programming

“…This fact leads us to the belief that any DCA sequence generated by the DC Algorithm also converges to a KKT point of (1). Our first attempts [22] showed that the above Conjecture 1 is true for the case where n = 2. The complete solution for Conjecture 1 in the present paper is obtained by combining Theorem 1.1 with the error bounds for affine variational inequalities due to Luo and Tseng [11].…”

“…In [23], it was shown that the DCA sequence generated by the projection DC decomposition algorithm applied to the problem of minimizing an indefinite quadratic form on a Euclidean ball converges to a KKT point. This fact leads us to the belief that any DCA sequence generated by the DC Algorithm also converges to a KKT point of (1).…”

Convergence of a Solution Algorithm in Indefinite Quadratic Programming

“…But there is a Conjecture [12, p. 489] saying that if the IQP has global solutions, then every DCA sequence generated by one of the algorithms A and B must be bounded. Recently, the Conjecture has been solved in the affirmative for the two-dimensional IQP by Tuan [25]. To solve it in the general case, Tuan [26] has used a local error bound for affine variational inequalities and several specific properties of the KKT point set of the IQP which were obtained by Luo and Tseng [15] (see also Tseng [24] and Luo [14]).…”