2012
DOI: 10.1007/s11590-012-0454-z
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Generalized Minty vector variational-like inequalities and vector optimization problems in Asplund spaces

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Cited by 20 publications
(10 citation statements)
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“…(i) If θ ≡ 0 and ∂ L f (·) = ∂ f (·), i.e., the Clarke subdifferential operator, then (P 2 ) and (P 3 ) reduces to nonsmooth exponential-type vector variational like inequality problem and nonsmooth exponential-type weak vector variational like inequality problem considered and studied by Jayswal and Choudhury [17]. (ii) For p = 0, a similar analogue of problems (P 2 ) and (P 3 ) was introduced and studied by Oveisiha and Zafarani [13].…”
Section: Definitionmentioning
confidence: 99%
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“…(i) If θ ≡ 0 and ∂ L f (·) = ∂ f (·), i.e., the Clarke subdifferential operator, then (P 2 ) and (P 3 ) reduces to nonsmooth exponential-type vector variational like inequality problem and nonsmooth exponential-type weak vector variational like inequality problem considered and studied by Jayswal and Choudhury [17]. (ii) For p = 0, a similar analogue of problems (P 2 ) and (P 3 ) was introduced and studied by Oveisiha and Zafarani [13].…”
Section: Definitionmentioning
confidence: 99%
“…Due to the fact that Clarke's subdifferentiability is bigger class than Mordukhovich limiting subdifferentiability, many authors studied the vector variational-like inequality problems and vector optimization problems by means of Mordukhovich limiting subdifferential. Later, Long et al [12] and Oveisiha and Zafarani [13] studied generalized vector variational-like inequality problem and discussed the relationships between generalized vector variational-like inequality problem and nonsmooth vector optimization problem for pseudoinvex mappings, whereas Chen and Huang [14] obtained similar results for invex mappings by means of Mordukhovich limiting subdifferential.…”
Section: Introductionmentioning
confidence: 99%
“…then we obtain parametric generalized vector quasi-variational-like inequality problem in [21]; (iv) if for each x, y ∈ A and p ∈ P, we define G(x, y, p) = 0, then (a) Problem (P β (p)) reduces to vector parametric equilibrium problems, which has been considered in, e.g., [9,10,11,12,13,17,22]; (b) if F(x, y, p) = H(y, p) − H(x, p), that H : A × P −→ 2 Z then, we have vector parametric optimization problem (see [16,18,23]); (c) if F(x, y, p) =< w, y − x >, such that T : A × P −→ 2 L(X,Z) and w ∈ T (x, p) then we obtain vector parametric variational inequality (see [23,24]).…”
Section: Introductionmentioning
confidence: 99%
“…Al-Homidan & Ansari (2010) gave such results for weak efficient solution of the nonsmooth vector optimization problem. Oveisiha & Zafarani (2013) established the relationship between vector variational-like inequality problems and nonsmooth vector optimization problems using α-invex function in Asplund spaces with limiting subdifferential.…”
Section: Introductionmentioning
confidence: 99%