A parallel subgradient projection algorithm for quasiconvex equilibrium problems under the intersection of convex sets

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

“…Examples of strongly quasiconvex functions which are not convex can be found in [18, 28,29,33,53,30]. For instance, the function x ∈ R n →…”

“…When employing them, there is no need to know the value of the Lipschitz-type condition parameter (which can be challenging to calculate in many situations), but the price to pay is that an extra gradient step is needed. For further details on this approach, see, for instance, [24,41] in the convex case and [53] in the quasiconvex setting (without inertial and relaxation effects).…”

“…Different proximal point type algorithms have been considered for solving equilibrium problems in the convex case, in some of them the employed bifunction being endowed with a generalized monotonicity property rather than the classical monotonicity. There are only a few (very recent) works where iterative methods for solving equilibrium problems with the underlying function (strongly) quasiconvex can be found, namely [28], where arguably the first proximal point method in such a framework is proposed; [52] with a subgradient method; [53] that contains a proximal subgradient algorithm and the recent contribution [4], which contains an extension of [28] to Bregman distances.…”