Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.11.2027.1.07

Volume 11, Issue 1, 1 February 2027, Pages 133-153

 

Abstract. In this paper, we introduce several variants of the most known notions of vector DC mappings defined on normed spaces, and we study their main properties and the relationships between them. These new variants are weaker than the usual concepts of vector DC mappings and involve DC decompositions interesting from a practical point of view. Then, we provide a characterization of approximate and exact proper efficient solutions, respectively, of a constrained vector DC optimization problem through linear scalarization and in terms of the classical subdifferential of Convex Analysis. The characterizations are also particularized to the finite dimensional setting, where the feasible set of the multiobjective DC optimization problem is given by inequality constraints. These results are generalizations to the vector case of the well-known characterizations of approximate and exact global minima of an unconstrained scalar DC optimization problem due to Hiriart-Urruty [J.B. Hiriart-Urruty, Generalized differentiability, duality and optimization for problems dealing with differences of convex functions, In: J. Ponstein, (eds) Convexity and Duality in Optimization, Lecture Notes in Econom. and Math. Systems, vol. 256, pp. 37-70, Springer, Berlin, Heidelberg, 1985].

 

How to Cite this Article:
L. Huerga, B. Jiménez, V. Novo, On DC mappings between normed spaces and applications in DC vector optimization, J. Nonlinear Var. Anal. 11 (2027), 133-153.