Based on the notion of relativemaximalmonotonicity, a hybrid proximal point algorithm is introduced and then it is applied to the approximation solvability of a general class of variational inclusion problems, while achieving a linear convergence. The obtained results generalize the celebrated work of Rockafellar (1976) where the Lipschitz continuity at 0 of the inverse of the set-valued mappin...

The purpose of this paper is to establish an existence result for nonconvex variational problems with Bochner integral constraints in separable Asplund spaces via the Euler–Lagrange inclusion, under the saturation hypothesis on measure spaces, which makes the Lyapunov convexity theorem valid in Banach spaces. The approach is based on the indirect method of the calculus of variations.

We establish variational principles for monotone and maximal bifunctions of Brøndsted-Rockafellar type by using our characterization of bifunction’s maximality in reflexive Banach spaces. As applications, we give an existence result of saddle point for convex-concave function and solve an approximate inclusion governed by a maximal monotone operator.

*Correspondence: [email protected] Department of Industrial Engineering, Anadolu University, Eskisehir, Turkey Institute of Control Systems, ANAS, Baku, Azerbaijan Abstract This paper is devoted to the optimal control problem of switching system in which constraints on the state variable are given by inclusions. Using Ekeland’s variational principle, second-order necessary condition of ...

Abstract For the purpose of this article, we introduce a modified form generalized system variational inclusions, called inclusion problems (GSMVIP). This problem reduces to classical and inequalities problems. Motivated by several recent results related subgradient extragradient method, propose new method for finding common element set solutions GSMVIP finite family Under suitable assumptions,...

A second-order variational inclusion for control systems under state constraints is derived and applied to investigate necessary optimality conditions for the Mayer optimal control problem. A new pointwise condition verified by the adjoint state of the maximum principle is obtained as well as a second-order necessary optimality condition in the integral form. Finally, a new sufficient condition...

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...