Sufficient Optimality Condition for Vector Optimization Problems under D.C. Data

Optimality Conditions for the Difference of Convex Set-Valued Mappings

“…For this aim, we use the concept of subdifferential of cone-convex set valued mappings recently introduced by Baier and Jahn [2]. Our technique extends the results obtained in scalar case by Hiriart-Urruty [10] and in vector case by Gadhi [7], Gadhi and Metrane [8], and Taa [19].…”

“…Genuinely, nonconvex mappings that arise in nonsmooth optimization are often of this type. Recently, extensive work on the analysis and optimization of D.C. mappings has been carried out [6,8,15,19]. However, much work remains to be done.…”

“…For more details on this notion, see [8] and [22]. When Y = R p and Z = R m , the problem (P 1 ) becomes…”

Optimization Problems With Difference of Set-Valued Maps Under Generalized Cone Convexity

“…the difference of convex mappings. This type of mappings has been studied in optimization theory in [7][8][9][10][12][13][14]. In 1989, Hiriart-Urruty [12] studied the D. C. optimization problems.…”

“…In 2009, Lahoussine et al [13] characterized the difference of locally Lipschitz D.C. mappings in terms of set-valued mapping monotonicity. In the last few years, authors like Flores-Bazán [7], Gadhi et al [9,10] and Taa [14] studied the optimization problems with the difference of cone convex vector-valued mappings. In 2005, Taa [14] established the optimality conditions for D.C. vector optimization problems by using the Lagrange-Fritz-John and Lagrange-Karush-Kuhn-Tucker multipliers rules.…”