Class Of Cost Functions Research Articles

Optimal organizational hierarchies in firms

Abstract One of the main problems in modern economy is to construct an efficient organizational hierarchy allowing to control the firm with minimal cost. This paper describes the mathematical model of optimal hierarchies in firms. Optimal hierarchies for several classes of cost functions are obtained. Particularly, sufficient conditions for tree optimality, 2hier‐archy (any manager has two immediate subordinates) optimality and two‐tier hierarchy optimality are defined.

Local Stabilization of the Navier–Stokes Equations with a Feedback Controller Localized in an Open Subset of the Domain

We study the local exponential stabilization, near a given steady-state flow, of solutions of the 2-D and 3-D Navier–Stokes equations in a bounded domain. The control is effectuated through a distributed control localized in an open subset of the domain. We apply a linear feedback controller, obtained by the solution of a control problem. Lyapunov functionals are given for a large class of cost functionals.

An optimal management hierarchy for given groups of executives

An important problem in economics is the construction of an effective minimal-cost management hierarchy for an economic system. A model for optimization of a management hierarchy is designed, a cost function is defined on a set of hierarchies consisting of exogenically given subdivisions (managers for supervising given groups), whereas other parts of a hierarchy may be formed arbitrarily and contain multiple subordination, etc. The optimal hierarchy for certain classes of cost functions is determined.

A Smoothing Method of Global Optimization that Preserves Global Minima

A new smoothing method of global optimization is proposed in the present paper, which prevents shifting of global minima. In this method, smoothed functions are solutions of a heat diffusion equation with external heat source. The source helps to control the diffusion such that a global minimum of the smoothed function is again a global minimum of the cost function. This property, and the existence and uniqueness of the solution are proved using results in theory of viscosity solutions. Moreover, we devise an iterative equation by which smoothed functions can be obtained analytically for a class of cost functions. The effectiveness and potential of our method are then demonstrated with some experimental results.

Interleaver Design for Serially Concatenated Convolutional Codes: Theory and Application

This paper addresses the problem of interleaver design for serially concatenated convolutional codes (SCCCs) tailored to the constituent codes of the SCCC configuration. We present a theoretical framework for interleaver optimization based on a cost function closely tied to the asymptotic bit-error rate (BER) of the block code C/sub s/ resulting from proper termination of the constituent codes in the SCCC code. We define a canonical form of the interleaving engine denoted as the finite state permuter (FSP) and using its structural property, develop a systematic iterative technique for construction of interleavers. The core theoretical results focus on the asymptotic behavior of a class of cost functions and their martingale property, which is then used to develop an order recursive interleaver optimization algorithm. We address the issue of the complexity of the interleaver growth algorithm presented in the paper and demonstrate that it has polynomial complexity. Subsequently, we provide details about the application of the proposed technique and present a modification of the algorithm that employs error pattern feedback for improved performance at a reduced complexity. Sample experimental results are provided for an SCCC code of rate 1/3 and information block length 320 that achieves a minimum distance of d/sub min/=44.

A Formula for the Derivative with Respect to Domain Variations in Navier--Stokes Flow Based on an Embedding Domain Method

Frechet differentiability and a formula for the derivative with respect to domain variation of a general class of cost functionals under the constraint of the two-dimensional stationary incompressible Navier--Stokes equations are shown. An embedding domain technique provides an equivalent formulation of the problem on a fixed domain and leads to a simple and computationally cheap line integral formula for the derivative of the cost functional with respect to domain variation. Existence of a solution to the corresponding domain optimization problems is proved. A numerical example shows the effectivity of the derivative formula.

Mixed serial cost sharing

A new serial cost sharing rule, called mixed serial cost sharing, is defined on the class of cost functions which equal a sum of an increasing convex and increasing concave function. This rule is based on a particular decomposition principle known as complementary-slackness decomposition and it coincides with the original serial rule of Moulin and Shenker (1992) [Moulin, H., Shenker, S., 1992. Serial cost sharing. Econometrica 60, 1009–1037] and the reversed serial rule of de Frutos (1998) [de Frutos, M.A., 1998. Decreasing serial cost sharing under economies of scale. Journal of Economic Theory 79, 245–275] if the cost function is convex or concave, respectively. The rule and its decomposition are characterized by three properties and the vector of payments is compared with existing cost sharing rules with respect to economic inequality measurement.

An Explicit Formula for the Derivative of a Class of Cost Functionals with Respect to Domain Variations in Stokes Flow

Domain optimization problems for the two-dimensional stationary Stokes equations are studied. Frechet differentiability of a class of cost functionals with respect to the variation of the shape of the computational domain is established. An embedding domain technique provides an equivalent formulation of the problem on a fixed domain and, moreover, a simply computable formula for the derivative of the cost functional with respect to the domain. Existence of a solution to the class of domain optimization problems is proved. Numerical examples show the reliability of the derivative formula.

Suboptimal control of rigid body motion with a quadratic cost

In this paper we consider the problem of controlling the rotational motion of a rigid body using three independent control torques. Given a quadratic cost we seek stabilizing state feedback controllers which guarantee that all motions starting within a specified bounded set have cost less than a given number; i.e., we seek suboptimal stabilizing controllers. For a special class of cost functions, we present explicit expressions for suboptimal stabilizing controllers yielding a cost arbitrarily close to the infimal cost. For the general case, we present sufficient conditions which guarantee the existence of linear, suboptimal, stabilizing controllers.

Regular flexibility of nested CES functions

In this paper we define the class of regular-flexible functional forms as the class of cost functions which are globally well-behaved and can provide a local approximation to any globally well-behaved cost function. We then offer a constructive proof of flexibility for the Nonseparable N-stage Constant-Elasticity-of-Substitution functional form (NNCES), by describing a technique through which the NNCES form can be parameterized so as to locally capture any regular configuration of input demands and second-order curvature conditions.

On indices of marginal and total production cost

In this paper we suggest cost indices that measure absolute changes in total and marginal production costs between two periods when factor prices change. The class of cost functions that generate equal total and marginal cost indices is characterized. A numerical illustration of the indices is provided using Indian cotton textile industry data.

A Note on One-Machine Scheduling Problems with Imperfect Information

In this paper we consider one-machine scheduling problems with or without a perfect machine and random processing times and derive among other results elimination criteria for different classes of cost functions.

Optimum Scan-Width Selection Under Containment Constraints

We consider the following algorithmic problem, which arises in connection with optimally choosing beam widths and positions for electron exposure of integrated circuit wafers. Let H > 0 be a fixed real number, and let c be a fixed, positive-valued, nondecreasing cost function defined on (0, H]. An instance of the problem consists of a given range R = [a, b] and n given intervals I i = [a i , b i ], 1 ≤ i ≤ n, each contained in R and of length not exceeding H. A solution (or feasible solution) for such an instance is a collection of segments, Si, S 2 , …, S k , each of length at most H and contained in R, such that each given interval is contained in at least one segment and the union of all the segments is R. The goal is to find an optimal solution with respect to c, i.e., a solution for which the sum of the costs of the individual segment lengths is as small as possible. The segments in a solution describe the beam positions and widths, projected on one side of the wafer, and the given intervals correspond to particularly sensitive regions on the layout mask, each of which must be entirely exposed by a single scan. The cost function gives the time required for a single scan of given width, including alignment overhead. Using dynamic programming techniques, we give efficient algorithms and data structures for solving this problem for several natural classes of cost functions, the most general of which is the class of all concave increasing functions, solved by an algorithm that runs in time O(n2).

A note on controlled diffusions on line with time-averaged cost

Existence of stable optimal Markov controls is established for a class of cost functions for controlled one-dimensional diffusions with time-averaged cost

Schedule Control For Randomly Drifting Production Sequences*

AbstractThis paper develops a model of control over a job sequence which drifts off schedule as the result of random variations in job processing times. Schedule integrity can be partially restored at extra cost by expediting jobs or halting production. The schedule deviation process is modelled as a Wiener process. Expediting production corresponds to a continually acting control on the process’ drift, while halting production corresponds either to an impulsive control or a non-stochastic drift control, depending on how the controller monitors the system. A complete solution to the average cost optimal policy is obtained for a class of cost functions in the impulsive representation of the problem. This is used to construct a partial solution to the problem in the more difficult mixed stochastic-deterministic representation.

A General Class of PAM Equalizers

This correspondence outlines a new and general class of cost functions which are applicable to adaptive PAM equalizer design. The new functions are shown to exhibit many of the features of well-known functions while promising lower receiver error probabilites. Further work in the area of relating cost functions to equalizer adaption rates is suggested.

Searching for a particle on the real line

In this paper we consider two optimization problems and two game problems. In each problem, a particle is hidden on the real line (sometimes randomly, and sometimes by an antagonistic hider), and a seeker, starting at the origin, wishes to find the particle with minimal expected cost. We consider a fairly wide class of cost functions depending upon the position of the particle and the time used to discover it. For the games we obtain the values and (∊-) optimal strategies. For the optimization problems we obtain qualitative features of (∊-) optimal searches.

Asymptotic properties of Bayes estimates of parameters of a signal masked by interference

It is shown that for a class of cost functions and a class of a priori distributions on the parameters to be estimated, the risks associated with the Bayes and maximum-likelihood estimates of the signal parameters become equal as the number of observations becomes large. This implies that the optimality properties usually attributed to Bayes estimates can be attributed in some cases to maximum-likelihood estimates as well. The work is an extension of known results to the case in which the statistical description of the observed process may be nonstationary.