WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 16, 2017
Minimum Principle Sufficiency for a Variational Inequality with Pseudomonotone Mapping
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Abstract: 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*є C*. One sufficient condition is also presented in terms of weaker sharpness of C*. With the psudomonotonicity* 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*.
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Keywords: Variational inequality, minimum principle sufficiency, weaker sharpness, pseudomonotonicity*, gap functions
Pages: 48-56
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 16, 2017, Art. #6