Preprint series: 07-06, Reports on Optimization and Stochastics

MSC:

47H05 Monotone operators (with respect to duality)

58C07 Continuity properties of mappings

47H04 Set-valued operators, See also {28B20, 54C60, 58C06}

Abstract: It is shown that a set-valued map M from a finite dimensional Hilbert space X into X is maximal monotone if and only if the following five conditions are satisfied: (i) M is monotone; (ii) M has a nearly convex domain; (iii) M is convex-valued; (iv) the recession cone of the values M(x) equals the normal cone to the closure of the domain of M at x; (v) M has a closed graph. We also show that the conditions (iii) and (v) can be replaced by Cesari's property (Q).

Keywords: monotone operators, semicontinuity, property (Q), maximal monotone

Upload: 2007-02-05

Update: 2007