Some relations between variational-like inequality problems and vectorial optimization problems in Banach spaces
نویسندگان
چکیده
In this work, we will establish some relations between variational-like inequality problems and vectorial optimization problems in Banach spaces under invexity hypotheses. This paper extends the earlier work of Ruiz-Garzón et al. [G. Ruiz-Garzón, R. OsunaGómez, A. Rufián-Lizana, Relationships between vector variational-like inequality and optimization problems, European J. Oper. Res. 157 (2004) 113–119]. c © 2007 Elsevier Ltd. All rights reserved.
منابع مشابه
Vector 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 کاملVector F -complementarity Problems with Nonconvex Preferences and Applications to Vector Optimization Problems
In this paper, several classes of vector F -complementarity problems (in short, VF -CP) and vector F -variational inequalities (in short, VF -VI) with relations determined by nonconvex preferences are introduced in Banach spaces. Some characterizations of solution sets for (VF -CP) and (VF -VI) are also presented. Furthermore, the results obtained are applied to vector optimization problems.
متن کاملSome relations between variational-like inequalities and efficient solutions of certain nonsmooth optimization problems
The connections between variational inequalities and optimization problems is well known, and many investigators have discussed them along many years; see, for instance, [1, 8, 10, 13]. This last article, which was authored by Giannessi, in particular, is one of the main works that study these connections in the finite-dimensional context. In recent years, the interest in the investigation on t...
متن کاملExistence of Solutions for Nonconvex and Nonsmooth Vector Optimization Problems
We consider the weakly efficient solution for a class of nonconvex and nonsmooth vector optimization problems in Banach spaces. We show the equivalence between the nonconvex and nonsmooth vector optimization problem and the vector variational-like inequality involving set-valued mappings. We prove some existence results concerned with the weakly efficient solution for the nonconvex and nonsmoot...
متن کاملKorpelevich's method for variational inequality problems in Banach spaces
We propose a variant of Korpelevich’s method for solving variational inequality problems with operators in Banach spaces. A full convergence analysis of the method is presented under reasonable assumptions on the problem data.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Computers & Mathematics with Applications
دوره 55 شماره
صفحات -
تاریخ انتشار 2008