463 Results Found

The purpose of this paper is to introduce a new algorithm to approximate a common solution for a system of generalized mixed equilibrium problems, split variational inclusion problems of a countable family of multivalued maximal monotone operators, a...

In this paper, we study a schematic approximation of solutions of a split null point problem for a finite family of maximal monotone operators in real Hilbert spaces. We propose an iterative algorithm that does not depend on the operator norm which s...

If X is a convex subset of a topological vector space and f is a real bifunction defined on $X\times X$, the problem of finding a point $x_0\in X$ such that $f(x_0,y)\ge 0$ for all $y\in X$, is called an equilibrium problem. When the bifunction f is define...

The aim of this paper is to present new existence results for solutions to a generalized quasi-equilibrium problem with set-valued mappings and moving cones. The key to this approach is a new Browder-type fixed point theorem, which permits working in...

The purpose of this article was to establish manifold versions of existence theorems for generalized vector quasi-equilibrium problems in locally compact and $\sigma$-compact spaces without any continuity assumption. The fixed-point theorem in a produ...

The aim of this paper is to propose an inertial-type AA-viscosity algorithm for approximating the common solutions of the split variational inclusion problem, the generalized equilibrium problem and the common fixed-point problem of nonexpansive mapp...

In this research, by means of the scalarization method, arcwise connectedness results were established for the sets of globally efficient solutions, weakly efficient solutions, Henig efficient solutions and superefficient solutions for the generalize...

This work develops and analyzes an iterative method to solve the combined generalized equilibrium and fixed point problems involving two relatively nonexpansive mappings. We establish that the generated sequence converges strongly to a shared solutio...

This paper is devoted to introducing a new viscosity approximation method using the implicit midpoint rules for finding a common element in the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a general system of v...

In this paper, two types of set-valued symmetric generalized strong vector quasi-equilibrium problems with variable ordering structures are discussed. By using the concept of cosmically upper continuity rather than the one of upper semicontinuity for...

The paper is devoted to bilevel problems: variational inequality problems over the set of solutions to the generalized equilibrium problems in a Hilbert space. To solve these problems, an iterative algorithm is proposed that combines the ideas of the...

In this work, we consider bilevel problems: variational inequality problems over the set of solutions of the generalized mixed equilibrium problems. Two new inertial extragradient methods are proposed for solving these problems. Under appropriate con...

We propose a multi-time generalized Nash equilibrium problem and prove its equivalence with a multi-time quasi-variational inequality problem. Then, we establish the existence of equilibria. Furthermore, we demonstrate that our multi-time generalized...

In this paper, based on the very recent work by Nandal et al. (Nandal, A.; Chugh, R.; Postolache, M. Iteration process for fixed point problems and zeros of maximal monotone operators. Symmetry 2019, 11, 655.), we propose a new generalized viscosity...

In this paper, our purpose is to investigate the vector equilibrium problem of whether the approximate solution representing bounded rationality can converge to the exact solution representing complete rationality. An approximation theorem is proved...

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-co...

In this paper, we establish new strong convergence theorems of proposed algorithms under suitable new conditions for the generalized split feasibility problem in Banach spaces. As applications, new strong convergence theorems for equilibrium problems...

Starting from some systems of vector equilibrium problems, we obtain the existence of the solution for a class of weighted equilibrium problems, under different types of generalized pseudo-monotonicity assumptions. We present both new and previous re...

Multistep composite implicit and explicit extragradient-like schemes are presented for solving the minimization problem with the constraints of variational inclusions and generalized mixed equilibrium problems. Strong convergence results of introduce...

A modified viscosity-type self-adaptive iterative algorithm is presented in this study, having a strong convergence theorem for estimating the common solution to the split generalized equilibrium problem along with the split common null point problem...

Nash Equilibrium (NE) plays a crucial role in game theory. The relaxation method in conjunction with the Nikaido–Isoda (NI) function, namely the NI-based relaxation method, has been widely applied to the determination of NE. Genetic Algorithm (...

Though many important links between the productivity/resource differences of countries and their trade patterns have been highlighted by traditional trade theories, much less attention has been devoted to studying the role of institutional quality in...

The aim of this paper is to show the existence and attainability of Karush–Kuhn–Tucker optimality conditions for weakly efficient Pareto points for vector equilibrium problems with the addition of constraints in the novel context of Hadam...

Equilibrium problems and variational inequalities are connected to the symmetry concepts, which play important roles in many fields of sciences. Some new preinvex functions, which are called generalized preinvex functions, with the bifunction $\zeta (.,.)$...

The purpose of this paper is to present a numerical method for solving a generalized equilibrium problem involving a Lipschitz continuous and monotone mapping in a Hilbert space. The proposed method can be viewed as an improvement of the Tseng’...

A plethora of applications from mathematical programming, such as minimax, and mathematical programming, penalization, fixed point to mention a few can be framed as equilibrium problems. Most of the techniques for solving such problems involve iterat...

A plethora of applications in non-linear analysis, including minimax problems, mathematical programming, the fixed-point problems, saddle-point problems, penalization and complementary problems, may be framed as a problem of equilibrium. Most of the...

We investigate the $\Delta$-convergence and strong convergence of a sequence generated by the proximal point method for pseudo-monotone equilibrium problems in Hadamard spaces. First, we show the $\Delta$-convergence of the generated sequence to a solu...

With the progress of society and the diversification of transportation modes, people are faced with more and more complicated travel choices, and thus, multi-criteria route choosing optimization problems have drawn increased attention in recent years...

In this review, we discuss the Dynamical approach to Non-Equilibrium Molecular Dynamics (D-NEMD), which extends stationary NEMD to time-dependent situations, be they responses or relaxations. Based on the original Onsager regression hypothesis, imple...

Hierarchical decision-making processes traditionally modeled as bilevel optimization problems are widespread in modern engineering and social systems. In this work, we deal with a leader with a population of followers in a hierarchical order of play....

The rotary double inverted pendulum system is characterized by one stable equilibrium point and three unstable equilibrium points due to its kinematic properties. This paper defines the transition control problem between these equilibrium points to e...

We consider non-equilibrium open statistical systems, subject to potentials and to external “heat baths” (hb) at thermal equilibrium at temperature T (either with ab initio dissipation or without it). Boltzmann’s classical equilibrium distributions g...

The well-known Noether theorem in Lagrangian and Hamiltonian mechanics associates symmetries in the evolution equations of a mechanical system with conserved quantities. In this work, we extend this classical idea to problems of non-equilibrium therm...

We consider a class of finite-dimensional variational inequalities where both the operator and the constraint set can depend on a parameter. Under suitable assumptions, we provide new estimates for the Lipschitz constant of the solution, which consid...

There is a debate if electricity markets on the basis of energy-only markets ensure a sufficient generation capacity. Various capacity mechanisms are discussed to tackle this potential problem. Capacity auctions with reliability options are seen as o...

This paper develops an algorithm for solving the generalized Nash equilibrium problem (GNEP) in non-cooperative games. The problem involves a set of players, each with a cost function that depends on their own decision as well as the decisions of oth...

The sensor coverage problem is a well-known combinatorial optimization problem that continues to attract the attention of many researchers. The existing game-based algorithms mainly pursue a feasible solution when solving this problem. This problem i...

With the rapid development of the Internet of Things, there are a series of security problems faced by the IoT devices. As the IoT devices are generally devices with limited resources, how to effectively allocate the restricted resources facing the s...

Classical thermodynamics employs the state of thermodynamic equilibrium, characterized by maximal disorder of the constituent particles, as the reference frame from which the Second Law is formulated and the definition of entropy is derived. Non-equi...

In this paper, we propose a generalized viscosity implicit iterative method for asymptotically non-expansive mappings in Banach spaces. The strong convergence theorem of this algorithm is proved, which solves the variational inequality problem. Moreo...

The development of artificial intelligence systems assumes that a machine can independently generate an algorithm of actions or a control system to solve the tasks. To do this, the machine must have a formal description of the problem and possess com...

This paper studies the cyclic dynamic gaming case of the r-interdiction median problem with fortification (CDGC-RIMF), which is important for strengthening a facility’s reliability and invulnerability under various possible attacks. We formulat...

In electricity markets, bilateral contracts (BC) are used to hedge against price volatility in the spot market. Pricing these contracts requires scheduling from either the buyer or the seller aiming to achieve the highest profit possible. Since this...

The uniqueness of equilibrium in bargaining games with three or more players is a problem preventing bargaining theory from general real world applications. We study the uniqueness of bargaining equilibrium in a bargaining game of two sellers and two...

This paper studies the problem of optimal channel design. For a given input probability distribution and for hard and soft design constraints, the aim here is to design a (probabilistic) channel whose output leaks minimally from its input. To analyse...

Almost every supplier faces uncertain and time-varying demand. E-commerce and online shopping have given suppliers unprecedented access to data on customers’ behavior, which sheds light on demand uncertainty. The main purpose of this research p...

The projected subgradient algorithms can be considered as an improvement of the projected algorithms and the subgradient algorithms for the equilibrium problems of the class of monotone and Lipschitz continuous operators. In this paper, we present an...

This paper investigates the structural properties of solutions of vector equilibrium systems and mixed variational inequalities in topological vector spaces. Based on Himmelberg-type fixed point theorem, combined with the analysis of set-valued mappi...

Many problems in practical engineering can be simplified as the cantilever beam model, which is generally studied by theoretical analysis, experiment, and numerical simulation. This paper discusses the local activity of the nonlinear nonplanar motion...