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Abstract: In this paper, we suggest and analyze a new inexact proximal point method for solving general variational inequalities, which can be considered as an implicit predictor–corrector method. An easily measurable error term is proposed with further relaxed error bound and an optimal step length is obtained by maximizing the profit-function and is dependent on the previous points. Our results include several known and new techniques for solving variational inequalities and related optimization problems. Results obtained in this paper can be viewed as an important improvement and refinement of the previously known results. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, we extend the classes of generalized type I vector-valued functions introduced by Aghezzaf and Hachimi in [J. Global Optim. 18 (2000) 91–101] to generalized univex type I vector-valued functions and consider a multiple-objective optimization problem involving generalized type I univex functions. A number of Kuhn–Tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution. The Mond–Weir and general Mond–Weir type duality results are also presented. [Copyright &y& Elsevier]