Showing papers by "Jong-Shi Pang published in 2009"
01 Jan 2009
160 citations
TL;DR: The goal of this article is to show how many challenging unsolved resource allocation problems in the emerging field of cognitive radio networks fit naturally either in the game theoretical paradigm or in the more general theory of VI.
Abstract: The goal of this article is to show how many challenging unsolved resource allocation problems in the emerging field of cognitive radio (CR) networks fit naturally either in the game theoretical paradigm or in the more general theory of VI This provides us with all the mathematical tools necessary to analyze the proposed equilibrium problems for CR systems (eg, existence and uniqueness of the solution) and to devise distributed algorithms along with their convergence properties
82 citations
TL;DR: An in-depth analysis of time-stepping methods for solving initial-value and boundary-value, non-Lipschitz linear complementarity systems (LCSs) under passivity and broader assumptions and shows that, using such least-norm solutions of the discrete-time subproblems, an implicit Euler scheme is convergent for passive initial- value LCSs.
Abstract: Generalizing recent results in [M. K. Camlibel, Complementarity Methods in the Analysis of Piecewise Linear Dynamical Systems, Ph.D. thesis, Center for Economic Research, Tilburg University, Tilburg, The Netherlands, 2001], [M. K. Camlibel, W. P. M. H. Heemels, and J. M. Schumacher, IEEE Trans. Circuits Systems I: Fund. Theory Appl., 49 (2002), pp. 349-357], and [J.-S. Pang and D. Stewart, Math. Program. Ser. A, 113 (2008), pp. 345-424], this paper provides an in-depth analysis of time-stepping methods for solving initial-value and boundary-value, non-Lipschitz linear complementarity systems (LCSs) under passivity and broader assumptions. The novelty of the methods and their analysis lies in the use of “least-norm solutions” in the discrete-time linear complementarity subproblems arising from the numerical scheme; these subproblems are not necessarily monotone and are not guaranteed to have convex solution sets. Among the principal results, it is shown that, using such least-norm solutions of the discrete-time subproblems, an implicit Euler scheme is convergent for passive initial-value LCSs; generalizations under a strict copositivity assumption and for boundary-value LCSs are also established.
63 citations
TL;DR: A generalized version of the existing iterative water-filling algorithm whereby the users and the jammer update their power allocations in a greedy manner is proposed, andSimulations show that when the convergence conditions are violated, the presence of a jammer can cause the, otherwise convergent, iterativeWater-Filling algorithm to oscillate.
Abstract: Consider a scenario in which K users and a jammer share a common spectrum of N orthogonal tones. Both the users and the jammer have limited power budgets. The goal of each user is to allocate its power across the N tones in such a way that maximizes the total sum rate that he/she can achieve, while treating the interference of other users and the jammer's signal as additive Gaussian noise. The jammer, on the other hand, wishes to allocate its power in such a way that minimizes the utility of the whole system; that being the total sum of the rates communicated over the network. For this noncooperative game, we propose a generalized version of the existing iterative water-filling algorithm whereby the users and the jammer update their power allocations in a greedy manner. We study the existence of a Nash equilibrium of this noncooperative game as well as conditions under which the generalized iterative water-filling algorithm converges to a Nash equilibrium of the game. The conditions that we derive in this paper depend only on the system parameters, and hence can be checked a priori. Simulations show that when the convergence conditions are violated, the presence of a jammer can cause the, otherwise convergent, iterative water-filling algorithm to oscillate.
60 citations
19 Apr 2009
TL;DR: A generalized version of the existing iterative water-filling algorithm whereby the users and the jammer update their power allocations in a greedy manner is proposed and conditions under which this algorithm converges to a Nash equilibrium of the game are studied.
Abstract: Consider a scenario in which K users and a jammer have a limited power budget and share a common spectrum of N orthogonal tones The goal of each user is to allocate its power across the N tones in such a way that maximizes the total sum rate that he/she can achieve, while treating the interference of other users and the jammer's signal as additive Gaussian noise The jammer, on the other hand, wishes to allocate its power in such a way that minimizes the utility of the whole system; that being the total sum of the rates communicated over the network For this non-cooperative game, we propose a generalized version of the existing iterative water-filling algorithm whereby the users and the jammer update their power allocations in a greedy manner We study conditions under which the generalized iterative water-filling algorithm converges to a Nash equilibrium of the game The conditions that we derive in this paper depend only on the system parameters, and hence can be checked a priori
37 citations