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The generalized Nash equilibriumproblem(GNEP) is anextensionof the standard Nash equilibrium problem(NEP), inwhich each player's strategy set may depend on the rival player's strategies. In this paper, we present two descent type methods. The algorithms are based on a reformulation of the generalized Nash equilibrium using Nikaido-Isoda function as unconstrained optimization. We prove that our algorithms are globally convergent and the convergence analysis is not based on conditions guaranteeing that every stationary point of the optimization problem is a solution of the GNEP. [ABSTRACT FROM AUTHOR]

We introduce a general iterative algorithm for finding a common element of the common fixedpoint set of an infinite family of ?i-strict pseudocontractions and the solution set of a general system of variational inclusions for two inverse strongly accretive operators in a q-uniformly smooth Banach space. Then, we prove a strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under very mild conditions. The methods in the paper are novel and different from those in the early and recent literature. Our results can be viewed as the improvement, supplementation, development, and extension of the corresponding results in some references to a great extent. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider a new scheme by the hybrid extragradient-like method for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality, and the set of fixed points of an infinitely family of strictly pseudocontractive mappings in Hilbert spaces. Then, we obtain a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm. Our results extend and improve the results of Issara Inchan 2010 and many others. [ABSTRACT FROM AUTHOR]

Under the condition that the values of mapping F are evaluated approximately, we propose a proximal analytic center cutting plane algorithm for solving variational inequalities. It can be considered as an approximation of the earlier cutting plane method, and the conditions we impose on the corresponding mappings are more relaxed. The convergence analysis for the proposed algorithm is also given at the end of this paper. [ABSTRACT FROM AUTHOR]

Recently, Xiao et al. proposed a nonsmooth equations-based method to solve the l₁-norm minimization problem (2011). The advantage of this method is its simplicity and lower storage. In this paper, based on new nonsmooth equations reformulation, we investigate new nonsmooth equations-based algorithms for solving l₁-norm minimization problems. Under mild conditions, we show that the proposed algorithms are globally convergent. The preliminary numerical results demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]