SUM OF MAXIMAL MONOTONE-OPERATORS REVISIT ED - THE CONCEPT OF VARIATIONAL SUM

The sum of (nonlinear) maximal monotone operators is reconsidered.from the Yosida approximation and graph-convergence point of view. This le ads to a new concept, called variational sum, which coincides with the classical (pointwise) sum when the classical sum happens to be maxima l monotone. In the case of subdifferentials of convex lower semicontin uous proper functions, the variational sum is equal to the subdifferen tial of the sum of the functions. A general feature of the variational sum is to involve not only the values of the two operators at the giv en point but also their values at nearby points.