Farkas-type results for fractional programming problems

Some Farkas-type results for fractional programming problems with DC functions

“…The fractional programming problem ( p) has been discussed in some recent papers as in [5].Thus it is easy to see that some previous results for the problem ( p) are the special cases of our results. In this section, the condition (C Q) is replaced by the following condition:…”

“…Next, we give an equivalent assertion to the statement (ii) in Theorem 4.1 by using the analogous method to the one in [5,7,11]. …”

“…As usual (also see [5]), we will denote by x T y = n i=1 x i y i the usual inner product of two vectors x = (x 1 , . .…”

“…Since the difference of two convex functions is not necessarily a convex function, the problem ( p λ ) is a nonconvex programming problem. In order to construct the dual problem to ( p λ ), we will use an approach inspired by DC programming (see [13] or [3,5,8]) and deal with it as two cases.…”

“…Recently, Boţ-Hodrea-Wanka presented in [5] some Farkas-type results for the fractional programming problems that the objective functions are the ratio of a convex function to a concave function with finitely many convex constraints. Inspired by their work, in this paper we will discuss the following fractional optimization problem with DC functions:…”