Showing papers on "Concave function published in 1987"
TL;DR: In this paper, the authors developed two methods for imposing curvature conditions globally in the context of cost function estimation, based on a generalization of a functional form first proposed by McFadden.
Abstract: Empirically estimated flexible functional forms frequently fail to satisfy the appropriate theoretical curvature conditions. Lau and Gallant and Golub have worked out methods for imposing the appropriate curvature conditions locally, but those local techniques frequently fail to yield satisfactory results. We develop two methods for imposing curvature conditions globally in the context of cost function estimation. The first method adopts Lau's technique to a generalization of a functional form first proposed by McFadden. Using this Generalized McFadden functional form, it turns out that imposing the appropriate curvature conditions at one data point imposes the conditions globally. The second method adopts a technique used by McFadden and Barnett, which is based on the fact that a non-negative sum of concave functions will be concave. Our various suggested techniques are illustrated using the U.S. Manufacturing data utilized by Berndt and Khaled
853 citations
TL;DR: This result is then applied to solve the optimal server allocation problem in a system of multi-server stations with a fixed buffer capacity, and for a single-station system, the simultaneous optimal allocation of both servers and buffer capacity is studied.
Abstract: Consider a closed queueing network Gordon and Newell [Gordon, W. J., G. F. Newell. 1967. Closed queueing networks with exponential servers. Oper. Res.15 252-267.] with a set of stations. The service rate at each station is an increasing concave function of the number of jobs at that station. Suppose there also exists a station that has c â¥1 parallel servers, each of which has a fixed service rate. We show that the throughput of this network is an increasing concave function with respect to c. This result is then applied to solve the optimal server allocation problem in a system of multi-server stations with a fixed buffer capacity for the total number of jobs at each station. For a single-station system, the simultaneous optimal allocation of both servers and buffer capacity is also studied.
130 citations
TL;DR: In this article, the authors studied the problem of allocation of the production rate among the m cells, such that the total throughput (over all m cells) will be maximised, while the blocking probabilities will be kept below a given set of limits.
Abstract: A manufacturing system capable of processing multiple part types generates input, at a given rate, R, to a set of m cells. Each cell processes a certain type of parts and has its own production and buffer capacities. We study the problem of aEocating the production rate, R, among the m cells, such that the total throughput (over all m cells) will be maximised, while the blocking probabilities willl be kept below a given set of limits. An optimisation problem is formulated, which maximises a concave function over a convex set. An algorithm is developed, which fuUy exploits the problem structure and efficiently generates the optimal solution. Several extensions of the model are also discussed.
55 citations
TL;DR: In this article, the authors define temporal convexity and concavity for continuous time stochastic processes and apply it to reliability theory, queueing theory, branching processes and record values.
37 citations
TL;DR: In this article, the authors present a method for finding the global minimum of a Lipschitzian function subject to a convex and a reverse convex constraint, which is the same complexity as the outer approximation algorithm for a concave minimization problem.
Abstract: We will present a new method for finding the global minimum of a Lipschitzian function under Lipschitzian constraints. The method consists in converting the given problem into one of globally minimizing a concave function subject to a convex and a reverse convex constraints. The resulting algorithm is of the same complexity as the outer approximation algorithm for a concave minimization problem.
21 citations
TL;DR: In this article, it was shown that a collection of continuous, non-negative, concave functions on R n+ can all be realized as parallel sections of a single continuous concave function ψ on R m+ for some m≧n.
17 citations
TL;DR: Raghavachari has shown the equivalence of zero-one integer programming and a concave quadratic penalty function for a sufficiently large value of the penalty, and shows that the results generalize to the case where the objective function is any concave function.
16 citations
TL;DR: In this paper, it is shown that the problem of resource allocation can be reduced to a single one-dimensional maximization of a differentiable concave function, and a simple graphical method is developed and applied to a family of well-known problems from the literature.
Abstract: The paper discusses a classical resource allocation problem. Using elementary arguments on Lagrangian duality it is shown that this problem can be reduced to a single one-dimensional maximization of a differentiable concave function. Moreover, a simple graphical method is developed and applied to a family of well-known problems from the literature.
14 citations
TL;DR: It is demonstrated that a special case of identical concave functions is solvable in O(m), and both results significantly improve the previous bounds for these problems.
7 citations
01 Oct 1987
TL;DR: In this paper, the Schurconcave and concave functions of the partial sums of nonnegative exchangeable random variables are studied, and two majorization inequalities are derived, and an application in reliability theory is discussed.
Abstract: : This paper contains inequalities for the exceptions of permutation-invariant concave functions of the partial sums of nonnegative exchangeable random variables. Two majorization inequalities are derived, and an application in reliability theory is discussed. Keywords: Concave and Schurconcave functions.
5 citations
01 Jan 1987
TL;DR: A branch and bound method is proposed for solving a very general class of global multiextremal decision problems where the objective is the sum of a convex and a concave function and the feasible set is the intersection of an convex set with the complement of a conveyed set.
Abstract: A branch and bound method is proposed for solving a very general class of global multiextremal decision problems where the objective is the sum of a convex and a concave function and the feasible set is the intersection of a convex set with the complement of a convex set.
01 Jan 1987
TL;DR: In this article, a geometrical approach is proposed for the case of cone-cylinder regression, in which the set of possible regression functions is the Cartesian product of a convex cone and a cylinder.
Abstract: Concave, isotonic, and Lipchitz regression analyses are examples of linear regression in which the coefficients are subject to linear restrictions. Computation of the maximum likelihood (normality) or least squares fit is available for the isotonic case in a bounded number of steps. For the concave case most of the algorithms have been difficult to implement or had no assured convergence; Dykstra (1983) gave an algorithm easy to implement and converging to the least squares solution as n→∞. Concave regression analysis is examined here from a geometrical viewpoint as a special case of cone-cylinder regression, in which the set of possible regression functions is the Cartesian product of a convex cone and a cylinder. The maximum likelihood/least squares solution is characterized in terms of geometrical properties of the cone-cylinder and the resulting computational procedure leads to the exact solution in a finite number of one dimensional projections.
01 Feb 1987
TL;DR: It has been shown by Fiacco that convexity or concavity of the optimal value of a parametric nonlinear programming problem can readily be exploited to calculate global parametric upper and lower bounds on the optimalvalue function.
Abstract: It has been shown by Fiacco that convexity or concavity of the optimal value of a parametric nonlinear programming problem can readily be exploited to calculate global parametric upper and lower bounds on the optimal value function. The approach is attractive because it involves manipulation of information normally required to characterize solution optimality. A procedure is briefly described for calculating and improving the bounds as well as its extensions to generalized convex and concave functions. Several areas of applications are also indicated.
TL;DR: An upper bound for the α for which D(f)α is a concave function off, wheref ranges over Minkowski-reduced positive definite quadratic forms with diagonal coefficients unity andD denotes the determinant off, was derived in this article.
Abstract: An upper bound is determined for the α for whichD(f)
α is a concave function off, wheref ranges over Minkowski-reduced positive definite quadratic forms inn variables with diagonal coefficients unity andD(f) denotes the determinant off In answer to a question of C E Nelson, it is shown thatD(f) is not concave in the casen ≥ 4
01 Jan 1987
TL;DR: In this article, a finite method for bilinear programming is given, which is based on an algorithm developed by Thoai [l6j] for the minimization of a concave function on a bounded polyhedron.
Abstract: In the paper a finite method for bilinear programming is given. It is based on an algorithm, which was developed by Thoai [l6j for the minimization of a concave function on a bounded polyhedron.