Remarks on a nonlinear complementarity problem
Journal of Optimization Theory and Applications
Journal of Optimization Theory and Applications
The linear order complementarity problem
Mathematics of Operations Research
Mathematical Programming: Series A and B
On the equivalence of nonlinear complementarity problems and least-element problems
Mathematical Programming: Series A and B
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This paper provides a systematic solvability analysis for (generalized) variational inequalities on separable Hilbert lattices. By contrast to a large part of the existing literature, our approach is lattice-theoretic, and is not based on topological fixed point theory. This allows us to establish the solvability of certain types of (generalized) variational inequalities without requiring the involved (set-valued) maps be hemicontinuous or monotonic. Some of our results generalize those obtained in the context of nonlinear complementarity problems in earlier work, and appear to have scope for applications. This is illustrated by means of several applications to fixed point theory, optimization, and game theory.