Alternative generalized Wolfe type and Mond-Weir type vector duality (Q2925028)

From the introduction: ``The main scope of this paper is to introduce new Wolfe and Mond-Weir type vector duals, achieved via the approach from [\textit{W. W. Breckner} and \textit{I. Kolumbán}, Mathematica, Cluj 10(33), 229--244 (1968; Zbl 0213.45102); Math. Scand. 25, 227--247 (1969; Zbl 0192.46703)] and [\textit{J. Jahn}, Vector optimization. Theory, applications, and extensions. Berlin: Springer (2004; Zbl 1055.90065)], to a general vector minimization problem. They consist of maximizing a vector subject to some constraints which contain the generalized Wolfe and respectively Mond-Weir scalar duals of the scalarized problem attached to the primal vector optimization problem. We compare these new vector duals with the vector duals from [\textit{R. I. Boţ} and \textit{S.-M. Grad}, J. Nonlinear Convex Anal. 12, No. 1, 81--101 (2011; Zbl 1214.49035)] and we deliver weak and strong duality statements for them. Then, we particularize the general problem to be constrained and unconstrained, respectively. For different vector perturbation functions we obtain new Wolfe and Mond-Weir type vector duals to these vector problems, extending thus the classes of problems for which these duality approaches can be applied. We compare the image sets of the different vector duals attached to the same vector optimization problem, delivering either inclusion relations between them, or counterexamples that prove that in general neither of them is a subset of the other.''