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In this study, we examine how the strategies of the players over multiple time scales impact the decision making, resulting payoffs and the costs in non-cooperative strategic games. We propose a dynamic generalized Nash equilibrium problem for non-cooperative strategic games which evolve in multidimensions. We also define an equivalent dynamic quasi-variational inequality problem. The existence of equilibria is established, and a spot electricity market problem is reformulated in terms of the proposed dynamic generalized Nash equilibrium problem. Employing the theory of projected dynamical systems, we illustrate our approach by applying it to a 39-bus network case, which is based on the New England system. Moreover, we illustrate a comparative study between multiple time scales and a single time scale by a simple numerical experiment. [ABSTRACT FROM AUTHOR]

Our study in this paper is focused on the split equality fixed-point problem with firmly quasi-non-expansive operators in infinite-dimensional Hilbert spaces. A self-adaptive simultaneous scheme is introduced, and its weak convergence is established under mild and standard assumptions. The new proposed scheme generalizes and extends some related works in the literature, and its simple structure makes it easy for implementation and numerical testing. Primary experiments presented in this paper, in finite- and infinite-dimensional spaces, emphasize their practical advantages over existing results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the multiple-sets split feasibility problem in real Hilbert space and propose a self-adaptive method that uses projections onto quadratic (balls) approximations of the problem's associated sets. Our algorithm has several major advantages over existing methods in the literature. The first is its simple implementation as it uses closed-formula projection onto balls, and the second is that strong convergence is obtained under mild conditions. Several numerical experiments illustrate and compare the performances of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, we examine how can one achieve equilibrium when two related non-cooperative strategic games are being played. We propose a split generalized Nash equilibrium problem for two non-cooperative strategic games and also define an equivalent split quasi-variational inequality problem. Further, by using the techniques of proving existence of quasi-variational inequality problems, we establish the existence of equilibria. Moreover, as an application, we investigate our split generalized Nash equilibrium problem in the terms of river basin pollution problem. [ABSTRACT FROM AUTHOR]

In this work we consider a bilevel equilibrium problem defined over the intersection of the fixed points set of demicontractive mappings. An inexact simultaneous projection method for solving the problem is introduced and its strong convergence is established under mild and standard conditions. Primary numerical illustrations in finite and infinite dimensional spaces with comparisons to related results in the literature, demonstrate the algorithm performances and emphasize its computational and theoretical advantages. [ABSTRACT FROM AUTHOR]

We study a feasibility‐seeking problem with percentage violation constraints (PVCs). These are additional constraints that are appended to an existing family of constraints, which single out certain subsets of the existing constraints and declare that up to a specified fraction of the number of constraints in each subset is allowed to be violated by up to a specified percentage of the existing bounds. Our motivation to investigate problems with PVCs comes from the field of radiation therapy treatment planning (RTTP) wherein the fully discretized inverse planning problem is formulated as a split feasibility problem and the PVCs give rise to nonconvex constraints. Following the CQ algorithm of Byrne (2002, Inverse Problems, Vol. 18, pp. 441–53), we develop a string‐averaging CQ‐method that uses only projections onto the individual sets that are half‐spaces represented by linear inequalities. The question of extending our theoretical results to the nonconvex sets case is still open. We describe how our results apply to RTTP and provide a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of bilevel multiple-sets split pseudomonotone equilibrium problems in real Hilbert spaces. A new parallel projection method is presented and a strong convergence theorem for solving the problem is established under mild assumptions. Our result is general and extends several existing results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we construct an evolutionary (time-dependent) split variational inequality problem and show how to reformulate equilibria of the dynamic traffic network models of two cities as such problem. We also establish existence result for the proposed model. Primary numerical results of equilibria illustrate the validity and applicability of our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two simple inertial algorithms for solving the split variational inclusion problem in Banach spaces. Under mild and standard assumptions, we establish the weak and strong convergence of the proposed methods, respectively. As theoretical realization we study existence of solutions of the split common fixed point problem in Banach spaces. Several numerical examples in finite and infinite dimensional spaces compare and illustrate the performances of our schemes. Our work generalize and extend some recent relate results in the literature and also propose a simple and applicable method for solving split variational inclusions. [ABSTRACT FROM AUTHOR]