TY - JOUR

T1 - Minimum principle sufficiency for a Variational inequality with Pseudomonotone mapping

AU - Wu, Zili

N1 - Funding Information:
Acknowledgements: The research was supported by RDF-15-02-31 of Xi’an Jiaotong-Liverpool University.

PY - 2017

Y1 - 2017

N2 - For a variational inequality problem (VIP) with a psudomonotone mapping F on its solution set C∗, we give equivalent statements for C∗ to be determined by the zeroes γ(C∗) of the primal gap function of VIP, where C∗ 2 C∗. One sufficient condition is also presented in terms of weaker sharpness of C∗. With the psudomonotonicityλ of F on C∗ being characterized, C∗ turns out to coincide with the zeroes λ(C∗) of the dual gap function of VIP. If also F has the same direction on γ(C∗), then γ(C∗) coincides with C∗, λ(C∗), and the solution set C∗ of the dual variational inequality problem. This has further been shown to be equivalent to saying that F is constant on γ(C∗) when F is psudomonotonone+ on C∗.

AB - For a variational inequality problem (VIP) with a psudomonotone mapping F on its solution set C∗, we give equivalent statements for C∗ to be determined by the zeroes γ(C∗) of the primal gap function of VIP, where C∗ 2 C∗. One sufficient condition is also presented in terms of weaker sharpness of C∗. With the psudomonotonicityλ of F on C∗ being characterized, C∗ turns out to coincide with the zeroes λ(C∗) of the dual gap function of VIP. If also F has the same direction on γ(C∗), then γ(C∗) coincides with C∗, λ(C∗), and the solution set C∗ of the dual variational inequality problem. This has further been shown to be equivalent to saying that F is constant on γ(C∗) when F is psudomonotonone+ on C∗.

KW - Gap functions

KW - Minimum principle sufficiency

KW - Pseudomonotonicity

KW - Variational inequality

KW - Weaker sharpness

UR - http://www.scopus.com/inward/record.url?scp=85033989527&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85033989527

SN - 1109-2769

VL - 16

SP - 48

EP - 56

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

ER -