Discrete Cost Function Research Articles

Optimal partition of QoS requirements with discrete cost functions

The future Internet is expected to support applications with quality of service (QoS) requirements. To this end, several mechanisms are suggested in the IETF; the most promising among them is DiffServ. An important problem in this framework is how to partition the QoS requirements of an application along a selected path. The problem which is, in general, NP-complete, was solved for continuous convex cost functions by Lorenz and Orda (see IEEE/ACM Trans. Networking. vol.6, p.768-78, 1998 and Proc. IEEE INFOCOM'99, p.246-53, 1999). This paper concentrates on discrete cost functions, which better model the existing and upcoming mechanisms in the Internet. We present efficient exact and approximated solutions for various conditions of the problem. We also show that although the more complex problem of QoS sensitive routing with discrete cost functions is hard, it has a fully polynomial approximation scheme.

Runge-Kutta methods in optimal control and the transformed adjoint system

The convergence rate is determined for Runge-Kutta discretizations of nonlinear control problems. The analysis utilizes a connection between the Kuhn-Tucker multipliers for the discrete problem and the adjoint variables associated with the continuous minimum principle. This connection can also be exploited in numerical solution techniques that require the gradient of the discrete cost function.

Intersample Performance Improvement in Generalized Predictive Control

Abstract The standard GPC is designed so that a discrete-time cost function is optimized. However, rather poor intersample performance may occur because the cost function in the discrete-time form cannot account for intersample behavior. Therefore, in this paper, a GPC design which can optimize the continuous response using a discrete-time control law with a Zero Order Hold (ZOH) is proposed. To this end, the discrete equivalent plant model and cost function are derived and the modified discrete-time GPC is solved. Finally, a numerical example is illustrated to show the effectiveness of the proposed method.

Parameter identification for a model of chromatographic column

Here we are interested in identifying the flux in a system of conservation laws. This problem is ill-posed, but we can deal with the indetermination by using an a priori problem as a constrained minimization of a cost function J. A Lagrangian formulation leads us to a formal computation of that gradient of J. We then perform an exact computation of the gradient of the discrete cost function. Finally, we give a few numerical results obtained through a conjugate gradient method.

Mapping DNA by stochastic relaxation: schedule for optimal annealing

The analysis of the various cooling schedules for the simulated annealing algorithm is made towards the restriction map construction. Algorithm behaviour under control of three different cost functions is considered and the discrete cost function is found to handle successfully experimental data with realistic error sizes. A program using this function has been derived from the algorithm to construct linear and circular DNA maps.

Optimal Plant Under Conditions of Risk

G. STIGLER2 has pointed out various problems of selecting an optimal plant when there is some uncertainty with respect to the level of competitive price. A different set of problems exist when there is uncertainty with respect to the amount that can be sold at a given price. It will be shown that the entrepreneur cannot select his optimal plant without explicit consideration of price, the probability distribution of demand, inventory level, and the discount rate. Indeed, an optimal dynamic production policy must be determined, indicating the optimal level of production for each level of initial inventory, before the optimal plant selection can be accomplished. The necessity of such a calculation points out the futility as well as the impossibility of separating the cost and demand components of economic analysis. Such a separation is futile if an optimization of profits that involves both aspects must be carried out before the cost component can be defined. Its impossibility is illustrated by numerical examples showing how the optimal plant varies in response to changes in the values of price, inventory, and the discount rate. It is incorrect to average costs over the probability distribution of demand as suggested by various authors. The model constructed is a stationary dynamic model with an infinite time horizon, a specified price, a specified discount rate, and two different plants, represented by two extremely simple, discrete cost functions. Demand is represented by a simple discrete probability distribution. The optimal production policy for each cost function as well as the discounted value of expected profits corresponding to each cost function was calculated by the use of R. A. Howard's dynamic programming technique.3 The entrepreneur is faced with a choice of two types of plant, one having a U-shaped average cost curve whose minimum contains the lowest possible average cost, while the other plant has a flatter cost curve with a higher minimum. The following example is a simple numerical illustration with the above properties. Although it is extremely oversimplified, the