D-gap Functions for a Class of Equilibrium Problems in Banach Spaces

By Igor V. Konnov, O. Pinyagina. 2003

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Abstract We consider rather a general class of equilibrium problems in a real Banach space, which involve nonsmooth convex functions. We apply the D-gap function approach to these problems and show that, under certain additional assumptions, they can be converted into a problem of finding a stationary point of a differentiable function. Based on this property, we suggest a descent type algorithm to find a solution to the initial problem. An example of applications to nonlinearly constrained equilibrium problems is also given.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

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