Lagrange Function

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Ping Zhang - One of the best experts on this subject based on the ideXlab platform.

  • secrecy optimized resource allocation for device to device communication underlaying heterogeneous networks
    IEEE Transactions on Vehicular Technology, 2017
    Co-Authors: Kecheng Zhang, Mugen Peng, Ping Zhang
    Abstract:

    Device-to-device (D2D) communications have recently attracted much attention for the potential capability to improve spectral efficiency (SE) underlaying the existing heterogeneous networks (HetNets). Due to no sophisticated control, D2D-worked user equipments (DUEs) themselves cannot resist eavesdropping or security attacks. It is urgent to maximize the secure capacity for both cellular users and DUEs. This paper formulates the radio resource-allocation problem to maximize the secure capacity of DUEs for D2D communication underlaying HetNets, which consist of high-power nodes (HPNs) and low-power nodes (LPNs). The optimization objective Function with transmit bit rate and power constraints, which is nonconvex and hard to directly derive, is first transformed into a matrix form. Then, the equivalent convex form of the optimization problem is derived according to Perron–Frobenius theory. A heuristic iterative algorithm based on the proximal theory is proposed to solve this equivalent convex problem through evaluating the proximal operator of the Lagrange Function. Numerical results show that the proposed radio resource-allocation solution significantly improves the secure capacity with a fast convergence speed.

  • Secrecy-Optimized Resource Allocation for Device-to-Device Communication Underlaying Heterogeneous Networks
    IEEE Transactions on Vehicular Technology, 2017
    Co-Authors: Kecheng Zhang, Mugen Peng, Ping Zhang, Xuelong Li
    Abstract:

    Device-to-device (D2D) communications recently have attracted much attention for its potential capability to improve spectral efficiency underlaying the existing heterogeneous networks (HetNets). Due to no sophisticated control, D2D user equipments (DUEs) themselves cannot resist eavesdropping or security attacks. It is urgent to maximize the secure capacity for both cellular users and DUEs. This paper formulates the radio resource allocation problem to maximize the secure capacity of DUEs for the D2D communication underlaying HetNets which consist of high power nodes and low power nodes. The optimization objective Function with transmit bit rate and power constraints, which is non-convex and hard to be directly derived, is firstly transformed into matrix form. Then the equivalent convex form of the optimization problem is derived according to the Perron-Frobenius theory. A heuristic iterative algorithm based on the proximal theory is proposed to solve this equivalent convex problem through evaluating the proximal operator of Lagrange Function. Numerical results show that the proposed radio resource allocation solution significantly improves the secure capacity with a fast convergence speed.

Kecheng Zhang - One of the best experts on this subject based on the ideXlab platform.

  • secrecy optimized resource allocation for device to device communication underlaying heterogeneous networks
    IEEE Transactions on Vehicular Technology, 2017
    Co-Authors: Kecheng Zhang, Mugen Peng, Ping Zhang
    Abstract:

    Device-to-device (D2D) communications have recently attracted much attention for the potential capability to improve spectral efficiency (SE) underlaying the existing heterogeneous networks (HetNets). Due to no sophisticated control, D2D-worked user equipments (DUEs) themselves cannot resist eavesdropping or security attacks. It is urgent to maximize the secure capacity for both cellular users and DUEs. This paper formulates the radio resource-allocation problem to maximize the secure capacity of DUEs for D2D communication underlaying HetNets, which consist of high-power nodes (HPNs) and low-power nodes (LPNs). The optimization objective Function with transmit bit rate and power constraints, which is nonconvex and hard to directly derive, is first transformed into a matrix form. Then, the equivalent convex form of the optimization problem is derived according to Perron–Frobenius theory. A heuristic iterative algorithm based on the proximal theory is proposed to solve this equivalent convex problem through evaluating the proximal operator of the Lagrange Function. Numerical results show that the proposed radio resource-allocation solution significantly improves the secure capacity with a fast convergence speed.

  • Secrecy-Optimized Resource Allocation for Device-to-Device Communication Underlaying Heterogeneous Networks
    IEEE Transactions on Vehicular Technology, 2017
    Co-Authors: Kecheng Zhang, Mugen Peng, Ping Zhang, Xuelong Li
    Abstract:

    Device-to-device (D2D) communications recently have attracted much attention for its potential capability to improve spectral efficiency underlaying the existing heterogeneous networks (HetNets). Due to no sophisticated control, D2D user equipments (DUEs) themselves cannot resist eavesdropping or security attacks. It is urgent to maximize the secure capacity for both cellular users and DUEs. This paper formulates the radio resource allocation problem to maximize the secure capacity of DUEs for the D2D communication underlaying HetNets which consist of high power nodes and low power nodes. The optimization objective Function with transmit bit rate and power constraints, which is non-convex and hard to be directly derived, is firstly transformed into matrix form. Then the equivalent convex form of the optimization problem is derived according to the Perron-Frobenius theory. A heuristic iterative algorithm based on the proximal theory is proposed to solve this equivalent convex problem through evaluating the proximal operator of Lagrange Function. Numerical results show that the proposed radio resource allocation solution significantly improves the secure capacity with a fast convergence speed.

Xuelong Li - One of the best experts on this subject based on the ideXlab platform.

  • Secrecy-Optimized Resource Allocation for Device-to-Device Communication Underlaying Heterogeneous Networks
    IEEE Transactions on Vehicular Technology, 2017
    Co-Authors: Kecheng Zhang, Mugen Peng, Ping Zhang, Xuelong Li
    Abstract:

    Device-to-device (D2D) communications recently have attracted much attention for its potential capability to improve spectral efficiency underlaying the existing heterogeneous networks (HetNets). Due to no sophisticated control, D2D user equipments (DUEs) themselves cannot resist eavesdropping or security attacks. It is urgent to maximize the secure capacity for both cellular users and DUEs. This paper formulates the radio resource allocation problem to maximize the secure capacity of DUEs for the D2D communication underlaying HetNets which consist of high power nodes and low power nodes. The optimization objective Function with transmit bit rate and power constraints, which is non-convex and hard to be directly derived, is firstly transformed into matrix form. Then the equivalent convex form of the optimization problem is derived according to the Perron-Frobenius theory. A heuristic iterative algorithm based on the proximal theory is proposed to solve this equivalent convex problem through evaluating the proximal operator of Lagrange Function. Numerical results show that the proposed radio resource allocation solution significantly improves the secure capacity with a fast convergence speed.

Mugen Peng - One of the best experts on this subject based on the ideXlab platform.

  • secrecy optimized resource allocation for device to device communication underlaying heterogeneous networks
    IEEE Transactions on Vehicular Technology, 2017
    Co-Authors: Kecheng Zhang, Mugen Peng, Ping Zhang
    Abstract:

    Device-to-device (D2D) communications have recently attracted much attention for the potential capability to improve spectral efficiency (SE) underlaying the existing heterogeneous networks (HetNets). Due to no sophisticated control, D2D-worked user equipments (DUEs) themselves cannot resist eavesdropping or security attacks. It is urgent to maximize the secure capacity for both cellular users and DUEs. This paper formulates the radio resource-allocation problem to maximize the secure capacity of DUEs for D2D communication underlaying HetNets, which consist of high-power nodes (HPNs) and low-power nodes (LPNs). The optimization objective Function with transmit bit rate and power constraints, which is nonconvex and hard to directly derive, is first transformed into a matrix form. Then, the equivalent convex form of the optimization problem is derived according to Perron–Frobenius theory. A heuristic iterative algorithm based on the proximal theory is proposed to solve this equivalent convex problem through evaluating the proximal operator of the Lagrange Function. Numerical results show that the proposed radio resource-allocation solution significantly improves the secure capacity with a fast convergence speed.

  • Secrecy-Optimized Resource Allocation for Device-to-Device Communication Underlaying Heterogeneous Networks
    IEEE Transactions on Vehicular Technology, 2017
    Co-Authors: Kecheng Zhang, Mugen Peng, Ping Zhang, Xuelong Li
    Abstract:

    Device-to-device (D2D) communications recently have attracted much attention for its potential capability to improve spectral efficiency underlaying the existing heterogeneous networks (HetNets). Due to no sophisticated control, D2D user equipments (DUEs) themselves cannot resist eavesdropping or security attacks. It is urgent to maximize the secure capacity for both cellular users and DUEs. This paper formulates the radio resource allocation problem to maximize the secure capacity of DUEs for the D2D communication underlaying HetNets which consist of high power nodes and low power nodes. The optimization objective Function with transmit bit rate and power constraints, which is non-convex and hard to be directly derived, is firstly transformed into matrix form. Then the equivalent convex form of the optimization problem is derived according to the Perron-Frobenius theory. A heuristic iterative algorithm based on the proximal theory is proposed to solve this equivalent convex problem through evaluating the proximal operator of Lagrange Function. Numerical results show that the proposed radio resource allocation solution significantly improves the secure capacity with a fast convergence speed.

K S Swarup - One of the best experts on this subject based on the ideXlab platform.

  • locational marginal pricing of reactive power in real time market considering voltage support requirement
    2019 9th International Conference on Power and Energy Systems (ICPES), 2019
    Co-Authors: Devika Jay, K S Swarup
    Abstract:

    Among the ancillary service markets for smooth real time operation of the system, reactive power support ancillary service market is regarded as one of the most important services. In this work, the total reactive power required in the system is formulated and based on the bids received from the market participants, value for reactive power is determined. Due to localised nature of reactive power, an assessment of local reactive power requirement is more effective and hence in this work, a localised reactive power market is formulated. The objective of system operator is to minimise value of reactive power in each local market such that optimal scheduling of reactive power generation is achieved subject to system constraints and voltage support. The value Function is formulated from the operation cost bids and lost opportunity cost bids (LOC) received from Generation Companies (GENCOs). From the Lagrange Function, locational marginal price (LMP) is then determined. The proposed localised reactive power market is tested on IEEE 24-Bus system. It is found that the localised reactive power market maintains sufficient reserve and provide better voltage support. The advantage of proposed pricing scheme is that, the generators are paid based on the value of reactive power requirement in the system determined locally, thereby reducing volatility of price and chance of exercising market power.

  • value based real time reactive power pricing model considering voltage security and reserve requirement
    Modern Electric Power Systems, 2019
    Co-Authors: Devika Jay, K S Swarup
    Abstract:

    Reactive power service is considered as an important ancillary service, due to its contribution towards maintaining system wide bus voltage. In this work, a value based reactive power pricing model suitable for real time market is proposed. In the proposed reactive power market model, bids(operation cost and lost opportunity cost(LOC) of reactive power) are received from the Generating Companies (GENCOs) participating in the real time market. From the bids received, a three component reactive power value Function is formulated. The components of value Function being load serving component, voltage support component and reserve component of reactive power requirement in the system. The objective of the Independent System Operator (ISO) is to minimise the value Function of reactive power requirement in the system subject to generator limits, bus voltage limits and transmission line limits. From the Lagrange Function of the optimisation problem, the marginal value (MV) of reactive power is derived to calculate the marginal price (MP) of reactive power. The NLP formulation of the market model is solved using DICOPT solver in GAMS and anlaysed on IEEE 24-Bus system. The simulation results prove that the proposed algorithm is efficient in clearing the reactive power market in such a way that the system wide bus voltage deviation is minimal and sufficient reactive power reserve is maintained in the network.