Cyclical monotonicity of maximal monotone step operators
Copyright policy )Cyclical monotonicity of maximal monotone step operators
Let X and Y be two locally convex Hausdorff topological vector spaces paired by a bilinear form \(\). A multimapping \(T: X\to 2^ y\) is said to be a locally step operator if each \(x\in X\) has a neighborhood U such that \(\{Ty\}_{y\in U}\) is a finite family of sets, that is, if locally T takes a finite number of set values. In this article it is shown that locally step operators that are at once maximal monotone are necessarily subdifferentials of locally polyhedral convex functions.
maximal monotone, Derivatives of functions in infinite-dimensional spaces, locally step operators, subdifferentials of locally polyhedral convex functions, bilinear form, Monotone operators and generalizations, locally convex Hausdorff topological vector spaces, multimapping
maximal monotone, Derivatives of functions in infinite-dimensional spaces, locally step operators, subdifferentials of locally polyhedral convex functions, bilinear form, Monotone operators and generalizations, locally convex Hausdorff topological vector spaces, multimapping
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