Minification

Abstract: The estimation of parameters in nonlinear algebraic models is considered for a general class of problems. Included are problems where both the independent and dependent variables are subject to error and problems where the model is algebraically implicit. The maximum likelihood principle leads to an equality constrained minimization problem. An algorithm to achieve this minimization is obtained through the use of Lagrange multipliers.

Abstract: We study how to use the BFGS quasi-Newton matrices to precondition minimization methods for problems where the storage is critical. We give an update formula which generates matrices using information from the last m iterations, where m is any number supplied by the user. The quasi-Newton matrix is updated at every iteration by dropping the oldest information and replacing it by the newest information. It is shown that the matrices generated have some desirable properties. The resulting algorithms are tested numerically and compared with several well-known methods.

Abstract: We investigate the problem of achieving global optimization for distributed channel selections in cognitive radio networks (CRNs), using game theoretic solutions. To cope with the lack of centralized control and local influences, we propose two special cases of local interaction game to study this problem. The first is local altruistic game, in which each user considers the payoffs of itself as well as its neighbors rather than considering itself only. The second is local congestion game, in which each user minimizes the number of competing neighbors. It is shown that with the proposed games, global optimization is achieved with local information. Specifically, the local altruistic game maximizes the network throughput and the local congestion game minimizes the network collision level. Also, the concurrent spatial adaptive play (C-SAP), which is an extension of the existing spatial adaptive play (SAP), is proposed to achieve the global optimum both autonomously as well as rapidly.

Abstract: Quasi-Newton methods accelerate the steepest-descent technique for function minimization by using computational history to generate a sequence of approximations to the inverse of the Hessian matrix. This paper presents a class of approximating matrices as a function of a scalar parameter. The problem of optimal conditioning of these matrices under an appropriate norm as a function of the scalar parameter is investigated. A set of computational results verifies the superiority of the new methods arising from conditioning considerations to known methods.