TY - JOUR
T1 - Relaxed-Inertial Proximal Point Algorithms for Nonconvex Equilibrium Problems with Applications
AU - Grad, Sorin Mihai
AU - Lara, Felipe
AU - Tintaya Marcavillaca, Raúl
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
PY - 2024/12/1
Y1 - 2024/12/1
N2 - 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.
AB - 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.
KW - Equilibrium problems
KW - Inertial algorithms
KW - Nonconvex optimization
KW - Proximal point algorithms
KW - Quasiconvexity
U2 - 10.1007/s10957-023-02375-1
DO - 10.1007/s10957-023-02375-1
M3 - Article
AN - SCOPUS:85184245346
SN - 0022-3239
VL - 203
SP - 2233
EP - 2262
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 3
ER -