منابع مشابه
Variational Sum of Monotone Operators
The sum of (nonlinear) maximal monotone operators is reconsidered from the Yosida approximation and graph-convergence point of view. This leads to a new concept, called variational sum, which coincides with the classical (pointwise) sum when the classical sum happens to be maximal monotone. In the case of subdiierentials of convex lower semicontinuous proper functions, the variational sum is eq...
متن کاملVisco-penalization of the sum of two monotone operators
A new type of approximating curve for finding a particular zero of the sum of two maximal monotone operators in a Hilbert space is investigated. This curve consists of the zeros of perturbed problems in which one operator is replaced with its Yosida approximation and a viscosity term is added. As the perturbation vanishes, the curve is shown to converge to the zero of the sum that solves a part...
متن کاملPartial regularization of the sum of two maximal monotone operators
— Tofind a zero of the sum of two maximal monotone operators, we analyze a twosteps algorithm where the problem is first approximated by a regularized one and the regularization parameter is then reduced to converge to a solution of the original problem. We give a formai proof of the convergence which, in that case, is not ergodic. The main resuit is a generalization of one given by Brezis [4] ...
متن کاملIterative Methods for the Sum of Two Monotone Operators
The set of solutions of 1.1 is denoted by A B −1 0 . A number of problems arising in structural analysis, mechanics, and economics can be studied in the framework of this kind of variational inclusions; see, for instance, 1–4 . The problem 1.1 includes many problems as special cases. 1 If B ∂φ : H → 2 , where φ : H → R ∪ ∞ is a proper convex lower semicontinuous function and ∂φ is the subdif an...
متن کاملGeneralized Solutions for the Sum of Two Maximally Monotone Operators
A common theme in mathematics is to define generalized solutions to deal with problems that potentially do not have solutions. A classical example is the introduction of least squares solutions via the normal equations associated with a possibly infeasible system of linear equations. In this paper, we introduce a “normal problem” associated with finding a zero of the sum of two maximally monoto...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1996
ISSN: 0026-2285
DOI: 10.1307/mmj/1029005463