The generalized Nash equilibrium problem （GNEP） is a generalization of the standard Nash equilibrium problem （NEP）, in which both the utility function and the strategy space of each player depend on the strategies...The generalized Nash equilibrium problem （GNEP） is a generalization of the standard Nash equilibrium problem （NEP）, in which both the utility function and the strategy space of each player depend on the strategies chosen by all other players. This problem has been used to model various problems in applications. However, the convergent solution algorithms are extremely scare in the literature. In this paper, we present an incremental penalty method for the GNEP, and show that a solution of the GNEP can be found by solving a sequence of smooth NEPs. We then apply the semismooth Newton method with Armijo line search to solve latter problems and provide some results of numerical experiments to illustrate the proposed approach.展开更多
Generalized Nash equilibrium problem （GNEP） is an important model that has many applications in practice. However, a GNEP usually has multiple or even infinitely many Nash equilibrium points and it is not easy to ch...Generalized Nash equilibrium problem （GNEP） is an important model that has many applications in practice. However, a GNEP usually has multiple or even infinitely many Nash equilibrium points and it is not easy to choose a favorable solution from those equilibria. This paper considers a class of GNEP With some kind of separability. We first extend the so-called normalized equilibrium concept to the stationarity sense and then, we propose an approach to solve the normalized stationary points by reformulating the GNEP as a single optimization problem. We further demonstrate the proposed approach on a GNEP model in similar product markets.展开更多
The electricity distribution network is experiencing a profound transformation with the concept of the smart grid,providing possibilities for selfish consumers to interact with the distribution system operator(DSO)and...The electricity distribution network is experiencing a profound transformation with the concept of the smart grid,providing possibilities for selfish consumers to interact with the distribution system operator(DSO)and to maximize their individual energy consumption utilities.However,this profitseeking behavior among consumers may violate the network constraints,such as line flows,transformer capacity and bus voltage magnitude limits.Therefore,a network-constrained energy consumption(NCEC)game among active load aggregators(ALAs)is proposed to guarantee the safety of the distribution network.The temporal and spatial constraints of an ALA are both considered,which leads the formulated model to a generalized Nash equilibrium problem(GNEP).By resorting to a well-developed variational inequality(VI)theory,we study the existence of solutions to the NCEC game problem.Subsequently,a two-level distributed algorithm is proposed to find the variational equilibrium(VE),a fair and stable solution to the formulated game model.Finally,the effectiveness of the proposed game model and the efficiency of the distributed algorithm are tested on an IEEE-33 bus system.展开更多
文摘The generalized Nash equilibrium problem （GNEP） is a generalization of the standard Nash equilibrium problem （NEP）, in which both the utility function and the strategy space of each player depend on the strategies chosen by all other players. This problem has been used to model various problems in applications. However, the convergent solution algorithms are extremely scare in the literature. In this paper, we present an incremental penalty method for the GNEP, and show that a solution of the GNEP can be found by solving a sequence of smooth NEPs. We then apply the semismooth Newton method with Armijo line search to solve latter problems and provide some results of numerical experiments to illustrate the proposed approach.
基金Supported by the National Natural Science Foundation of China(Grant No.11071028)
文摘Generalized Nash equilibrium problem （GNEP） is an important model that has many applications in practice. However, a GNEP usually has multiple or even infinitely many Nash equilibrium points and it is not easy to choose a favorable solution from those equilibria. This paper considers a class of GNEP With some kind of separability. We first extend the so-called normalized equilibrium concept to the stationarity sense and then, we propose an approach to solve the normalized stationary points by reformulating the GNEP as a single optimization problem. We further demonstrate the proposed approach on a GNEP model in similar product markets.
基金This work was supported in part by the Science and Technology Project of SGCC“Research on Morphologies and Pathways of Future Power System”。
文摘The electricity distribution network is experiencing a profound transformation with the concept of the smart grid,providing possibilities for selfish consumers to interact with the distribution system operator(DSO)and to maximize their individual energy consumption utilities.However,this profitseeking behavior among consumers may violate the network constraints,such as line flows,transformer capacity and bus voltage magnitude limits.Therefore,a network-constrained energy consumption(NCEC)game among active load aggregators(ALAs)is proposed to guarantee the safety of the distribution network.The temporal and spatial constraints of an ALA are both considered,which leads the formulated model to a generalized Nash equilibrium problem(GNEP).By resorting to a well-developed variational inequality(VI)theory,we study the existence of solutions to the NCEC game problem.Subsequently,a two-level distributed algorithm is proposed to find the variational equilibrium(VE),a fair and stable solution to the formulated game model.Finally,the effectiveness of the proposed game model and the efficiency of the distributed algorithm are tested on an IEEE-33 bus system.
