Relaxed-Inertial Proximal Point Algorithms for Nonconvex Equilibrium Problems with Applications

Sorin-Mihai Grad (), Felipe Lara () and Raúl Tintaya Marcavillaca ()
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Sorin-Mihai Grad: Institut Polytechnique de Paris
Felipe Lara: Universidad de Tarapacá
Raúl Tintaya Marcavillaca: Universidad de Tarapacá

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 3, No 6, 2233-2262

Abstract: Abstract We propose a relaxed-inertial proximal point algorithm for solving equilibrium problems involving bifunctions which satisfy in the second variable a generalized convexity notion called strong quasiconvexity, introduced by Polyak (Sov Math Dokl 7:72–75, 1966). The method is suitable for solving mixed variational inequalities and inverse mixed variational inequalities involving strongly quasiconvex functions, as these can be written as special cases of equilibrium problems. Numerical experiments where the performance of the proposed algorithm outperforms one of the standard proximal point methods are provided, too.

Keywords: Proximal point algorithms; Inertial algorithms; Equilibrium problems; Nonconvex optimization; Quasiconvexity (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-023-02375-1

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