scholarly journals Existence theory for the complex linear complementarity problem

1972 ◽  
Vol 40 (3) ◽  
pp. 738-762 ◽  
Author(s):  
Charles J McCallum
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Existence Theory ◽  
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 ◽  
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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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