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On the difference of two maximal monotone operators. (English) Zbl 0811.47053

Summary: For the problem of finding a zero of the difference of two maximal monotone operators, we consider the regularization of these operators, via approximate of Yosida, and then we establish the relationship between these two problems. Also, we point out an evident application of this subject to d.c. programming (difference of two convex functions), when the maximal monotone operators are subdifferentials of lower semicontinuous proper convex functions.

MSC:

47H05 Monotone operators and generalizations
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
49J52 Nonsmooth analysis
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