Vector nonsmooth variational-like inequalities and optimization problems (original) (raw)

Vector optimization and variational-like inequalities

2009

In this paper, some properties of pseudoinvex functions are obtained. We study the equivalence between different solutions of the vector variational-like inequality problem. Some relations between vector variational-like inequalities and vector optimization problems for non-differentiable functions under generalized monotonicity are established.

On optimality conditions for vector variational inequalities

2014

Optimality conditions for weak efficient, global efficient and efficient solutions of vector variational inequalities with constraints defined by equality, cone and set constraints are derived. Under various constraint qualifications, necessary optimality conditions for weak efficient, global efficient and efficient solutions in terms of the Clarke and Michel-Penot subdifferentials are established. With assumptions on quasiconvexity of constraint functions sufficient optimality conditions are also given.

Vector variational-like inequality problem and vector optimization problem

Applied Mathematics Letters, 2010

α-invex function Strictly α-invex function Pseudo-α-invex function α-invex set Directionally differentiable function a b s t r a c t In this paper, we consider (weak) vector variational-like inequality problems ((W)VLIP) and (weak) vector optimization problems ((W)VOP), and check their relationships through the existence of solutions in topological vector spaces.

Generalized vector variational-like inequalities and vector optimization

2012

In this paper, we consider different kinds of generalized vector variational-like inequality problems and a vector optimization problem. We establish some relationships between the solutions of generalized Minty vector variational-like inequality problem and an efficient solution of a vector optimization problem. We define a perturbed generalized Stampacchia vector variational-like inequality problem and discuss its relation with generalized weak Minty vector variational-like inequality problem. We establish some existence results for solutions of our generalized vector variational-like inequality problems.

Some relations between variational-like inequality problems and vectorial optimization problems in Banach spaces

Computers & Mathematics with Applications, 2008

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. Osuna-Gómez, A. Rufián-Lizana, Relationships between vector variational-like inequality and optimization problems, European J. Oper. Res. 157 (2004) 113-119].

On vector variational-like inequality problems

Journal of Mathematical Analysis and Applications, 2005

In this paper, we establish some relationships between vector variational-like inequality and vector optimization problems under the assumptions of α-invex functions. We identify the vector critical points, the weakly efficient points and the solutions of the weak vector variational-like inequality problems, under pseudo-α-invexity assumptions. These conditions are more general than those of existing ones in the literature. In particular, this work extends the earlier work of Ruiz-Garzon et al. [G. Ruiz-Garzon, R. Osuna-Gomez, A. Rufian-Lizan, Relationships between vector variational-like inequality and optimization problems, European J. Oper. Res. 157 (2004) 113-119] to a wider class of functions, namely the pseudo-α-invex functions studied in a recent work of Noor [M.A. Noor, On generalized preinvex functions and monotonicities,