An Existence Theorem for the Complex Linear Complementarity Problem

1979 ◽  
Vol 59 (6) ◽  
pp. 275-276
Author(s):  
J Parida ◽  
K. C. Nayak
Keyword(s):  
Existence Theorem ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Complex Linear

scholarly journals On the complex complementarity problem

1973 ◽  
Vol 9 (2) ◽  
pp. 249-257 ◽  
Author(s):  
Bertram Mond
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Convex Cone ◽  
Complex Space ◽  
Linear Complementarity ◽  
Polar Cone ◽  
Polyhedral Convex ◽  
Complex Linear ◽  
Image Position

The complex linear complementarity problem considered here is the following: Find z such thatwhere S is a polyhedral convex cone in Cp, S* the polar cone, M ∈ Cp×p and q ∈ Cp.Generalizing earlier results in real and complex space, it is shown that if M satisfies RezHMz ≥ 0 for all z ∈ Cp and if the set satisfying Mz + q ∈ S*, z ∈ S is not empty, then a solution to the complex linear complementarity problem exists. If RezHMz > 0 unless z = 0, then a solution to this problem always exists.

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