Abstract
In this work, we prove weak convergence of a single-step iterative algorithm to a solution of variational inequality problems in 2-uniformly convex and uniformly smooth real Banach spaces. We apply our main result to the Nash-Cournot equilibrium oligopoly electricity market. We also give some numerical examples in infinite dimensional setting to illustrate how our algorithm works. Finally, our results generalize and complement several existing results in the literature.
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The authors appreciate the support of their institution and AfDB.
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This work is supported from AfDB Research Grant Funds to AUST.
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Bello, A.U., Yusuf, H. & Djitte, N. Single-step algorithm for variational inequality problems in 2-uniformly convex banach spaces. Rend. Circ. Mat. Palermo, II. Ser 72, 1463–1481 (2023). https://doi.org/10.1007/s12215-022-00746-7
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DOI: https://doi.org/10.1007/s12215-022-00746-7