الگوريتم هاي نقطه تقريبي براي مسائل تعادلي يكنوانماي شبه محدب

In this thesis, it is proven that every strongly quasiconvex function is 2-supercoercive (coercive). The usual properties of proximal operators for strongly quasiconvex functions are then, investigated. Additionally, it is demonstrated that the set of fixed points of the proximal operator coincides with the unique minimizer of a lower semicontinuous strongly quasiconvex function. Furthermore, the proximal point algorithm for finding the unique solution to the minimization problem of a strongly quasiconvex function is proven, using a positive sequence of parameters bounded away from zero. The general quasiconvex case is also revisited. A relationship between strongly quasiconvex functions an‎d strictly pseudoconvex functions is established. Finally, a proximal point method for quasiconvex pseudomonotone equilibrium problems is proposed. The subproblems of this method are optimization problems, where the objective is the sum of a strongly quasiconvex function an‎d the stan‎dard quadratic regularization term. Under suitable additional assumptions, the convergence of the generated sequence to a solution of the equilibrium problem is proposed, whenever the bifunction is strongly quasiconvex in its second argument.

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