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Positive vector complementarity problem (PVCP): finding such that.
(Weak) vector complementarity problem (VCP): finding such that (1.1).
Strong vector complementarity problem (SVCP): finding such that.
Generalized positive vector complementarity problem (GPVCP): finding and such that (1.5).
Generalized strong vector complementarity problem (GSVCP): finding and such that (1.6).
The generalized positive vector complementarity problem (GPVCP): finding such that (3.34).
(Weak) generalized vector complementarity problem (GVCP): finding and such that (1.4).
(iii)The generalized vector complementarity problem (GVCP): finding such that where is associated with in the definition of.
It is well known that if K is a closed convex cone, then (operatorname {VI}(T,K)) is equivalent to the nonlinear complementarity problem of finding (u^ in K) such that Tbigl u^bigr) in K^quad mbox{and} quad bigllangle Tbigl u^bigr), u bigrrangle = 0, (2) where (K^ := { y inmathbb{R}^{n}: langle y,x ranglegeq0 mbox{ for all } x in K }).
Such a problem is connected with the convex minimization problem, the complementarity, the problem of finding a point satisfying, and so on.
In this paper, we consider the following linear complementarity problem (LCP) of finding u ∈ R n such that u ≥ 0, F ( u ) ≥ 0, u T F ( u ) = 0, (1.1).
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