2021/12/07 by Yen, Le Hai, Muu, Le Dung
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2112.03483
We attempt to provide an algorithm for approximating a solution of the quasiconvex equilibrium problem that was proved to exist by K. Fan 1972. The proposed algorithm is an iterative procedure, where the search direction at each iteration is a normal-subgradient, while the step-size is updated avoiding Lipschitz-type conditions. The algorithm is convergent to a ρ- quasi-solution with any positive ρ if the bifunction f is semistrictly quasiconvex in its second variable, while it converges to the solution when f is strongly quasiconvex. Neither monotoniciy nor Lipschitz property is required.