Electrical and Electronic Engineering - Research Publications

Permanent URI for this collection

http://hdl.handle.net/11343/362

Filters

2015 - 2016 2
Reset filters

Settings
Statistics
Citations
Author: Alpcan, Tansu × Author: NEKOUEI, EHSAN × Author: Nair, Girish × End date: 2019 × Start date: 2010 × Type: Conference Paper ×

Search Results

Now showing 1 - 2 of 2
  • Item
    Thumbnail Image
    Convergence Analysis of Quantized Primal-dual Algorithm in Quadratic Network Utility Maximization Problems
    Nekouei, E ; NAIR, G ; Alpcan, T (IEEE, 2015)
    This paper examines the effect of quantized communications on the convergence behavior of the primal-dual algorithm in quadratic network utility maximization problems with linear equality constraints. In our set-up, it is assumed that the primal variables are updated by individual agents, whereas the dual variables are updated by a central entity, called system, which has access to the parameters quantifying the system-wide constraints. The notion of differential entropy power is used to establish a universal lower bound on the rate of exponential mean square convergence of the primal-dual algorithm under quantized message passing between agents and the system. The lower bound is controlled by the average aggregate data rate under the quantization, the curvature of the utility functions of agents, the number of agents and the number of constraints. An adaptive quantization scheme is proposed under which the primal-dual algorithm converges to the optimal solution despite quantized communications between agents and the system. Finally, the rate of exponential convergence of the primal-dual algorithm under the proposed quantization scheme is numerically studied.
  • Item
    Thumbnail Image
    Lower Bounds on the Best-Case Complexity of Solving a Class of Non-cooperative Games
    Nekouei, E ; Alpcan, T ; Nair, GN ; Evans, RJ (Elsevier, 2016)
    This paper studies the complexity of solving the class G of all N-player non-cooperative games with continuous action spaces that admit at least one Nash equilibrium (NE). We consider a distributed Nash seeking setting where agents communicate with a set of system nodes (SNs), over noisy communication channels, to obtain the required information for updating their actions. The complexity of solving games in the class G is defined as the minimum number of iterations required to find a NE of any game in G with ε accuracy. Using information-theoretic inequalities, we derive a lower bound on the complexity of solving the game class G that depends on the Kolmogorov 2ε-capacity of the constraint set and the total capacity of the communication channels. We also derive a lower bound on the complexity of solving games in G which depends on the volume and surface area of the constraint set.