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- W2890069019 abstract "Algorithms for solving the Ky Fan inequality EP(f, C) are tackled exploiting the tools developed in the previous chapter. Some assumptions on C and f hold throughout all the chapter in order to provide a unified algorithmic framework. Precisely, C is supposed to be convex and closed, f to be continuous and to satisfy f(x, x) = 0 for any $$xin mathbb {R}^n$$ while f(x, ⋅) to be τ-convex Convexity -convex function for any $$xin mathbb {R}^n$$ for some τ ≥ 0 that does not depend upon the considered point x. Notice that this framework guarantees all the assumptions of the existence Theorems 2.3.4 and 2.3.8 except for the boundedness of C or some kind of monotonicity of f. Indeed, all the algorithms require at least one of them, so that the existence of a solution is always guaranteed." @default.
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- W2890069019 date "2018-09-21" @default.
- W2890069019 modified "2023-10-17" @default.
- W2890069019 title "Algorithms for Equilibria" @default.
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- W2890069019 doi "https://doi.org/10.1007/978-3-030-00205-3_3" @default.
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