Vector and Ordered Variational Inequalities and Applications to Order-Optimization Problems on Banach Lattices
نویسندگان
چکیده
منابع مشابه
Ordered Variational Inequalities and Ordered Complementarity Problems in Banach Lattices
and Applied Analysis 3 Lemma 3. Let (X; ≽) be a Banach lattice. Then the positive coneX is weakly closed. Proof. It is clear that the positive coneX of the Banach lattice X is convex. We have mentioned that the positive coneX of the Banach latticeX is norm closed. ApplyingMazur’s lemma (see [12] or [15]), we have in a Banach space, a convex set is norm closed if and only if it is weakly closed....
متن کاملVector Optimization Problems and Generalized Vector Variational-Like Inequalities
In this paper, some properties of pseudoinvex functions, defined by means of limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality, the Stampacchia vector variational-like inequality, and the weak formulations of these two inequalities defined by means of limiting subdifferential are studied. Moreover, some relationships between the vector vari...
متن کاملOn composite vector variational-like inequalities and vector optimization problems
In this paper, we present the concept of generalized invexity for vector-valued functions. Also, we consider different kinds of generalized vector variational-like inequality and a vector optimization problem. Some relations between vector variational-like inequalities and a vector optimization problem are established by using the properties of Mordukhovich limiting subdifferential. Acknowledge...
متن کاملPseudoconvex Multiobjective Continuous-time Problems and Vector Variational Inequalities
In this paper, the concept of pseudoconvexity and quasiconvexity for continuous~-time functions are studied and an equivalence condition for pseudoconvexity is obtained. Moreover, under pseudoconvexity assumptions, some relationships between Minty and Stampacchia vector variational inequalities and continuous-time programming problems are presented. Finally, some characterizations of the soluti...
متن کاملWell-posed Vector Optimization Problems and Vector Variational Inequalities
In this paper we introduce notions of well-posedness for a vector optimization problem and for a vector variational inequality of differential type, we study their basic properties and we establish the links among them. The proposed concept of well-posedness for a vector optimization problem generalizes the notion of well-setness for scalar optimization problems, introduced in [2]. On the other...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2013
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2013/439394