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Volume 3, Issue 2, 31 August 2021, Pages 297-314
Abstract. We introduce a new concept of approximate solutions to quasi-equilibrium problems (QEP) conceived as approximate fixed points of the implicit selection map associated with this problem. As an application, we consider quasivariational inequalities (QVI) for which we discuss several types of approximations from regularization perspectives to devise a consequential term of approximate solutions. Then we present sensitivity analysis results for parametric versions of (QEP) and (QVI) wherein a recent approximate version of the well-known Lim’s Lemma is employed to obtain quantitative stability of approximate solutions to these problems. We finally emphasize that the proposed approximate quasi-equilibrium points converge, from both of the qualitative and quantitative stability aspects, to exact solutions. As a further consequence, we improve some previous stability results of solutions to traffic networks problems with respect to feasible flows under perturbation.
How to Cite this Article:
Mohamed Ait Mansour, Mohamed Amin Bahraoui, Adham El Bekkali, Approximate solutions of quasi-equilibrium problems: Lipschitz dependence of solutions on parameters, J. Appl. Numer. Optim. 3 (2021), 297-314.