Abstract
The auxiliary problem principle was used to derive many iterative type of algorithms in order to solve optimal control problems, mathematical programming and variational inequalities. In the present paper, we use this principle combined with a generalized Tikhonov method to introduce and study new general methods in order to solve nonlinear variational problems. We do not assume that the monotone operator involved in the general variational problem is strongly monotone or is co-coercive. Moreover, we take advantage of this combination to construct iterative methods which allow us to select a particular element of the solution set.
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Moudafi, A., Théra, M. (1997). Combining the Auxilliary Problem Principle with Approximation Methods. In: Gritzmann, P., Horst, R., Sachs, E., Tichatschke, R. (eds) Recent Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59073-3_14
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DOI: https://doi.org/10.1007/978-3-642-59073-3_14
Publisher Name: Springer, Berlin, Heidelberg
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