Lĩnh vực Toán ứng dụng (11)

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  • Bài báo/Newspaper

  • Authors: V. Jeyakumar (1999)

  • Noncompact convexificators, which provide upper convex and lower concave approximations for a continuous function, are defined. Various calculus rules, including extremality and mean-value properties, are presented. Regularity conditions are given for convexi ficators to be minimal. A characterization of quasiconvexity of a con tinuous function is obtained in terms of the quasimonotonicity of convexificators.

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  • Bài báo/Newspaper

  • Authors: V. Jeyakumar (1998)

  • The notion of approximate Jacobian matrices is introduced for a continuous vector valued map. It is shown, for instance, that the Clarke generalized Jacobian is an approximate Jacobian for a locally Lipschitz map. The approach is based on the idea of convexificators of real valued functions. Mean value conditions for continuous vector-valued maps and Taylor’s expansions for continuously Gˆateaux differentiable functions (i.e., C1-functions) are presented in terms of ap proximate Jacobians and approximate Hessians, respectively. Second-order necessary and sufficient conditions for optimality and convexity of C1-functions are also given

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  • Bài báo/Newspaper

  • Authors: B. Aghezzaf (1999)

  • In this paper, we develop second-order necessary and sufficient optimality conditions for multiobjective optimization problems with both equality and inequality constraints. First, we generalize the Lin fundamental theorem (Ref. 1) to second-order tangent sets; then, based on the above generalized theorem, we derive second-order neces sary and sufficient conditions for efficiency.

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  • Authors: Do Van Luu (2009)

  • In this article, we establish theorems of the alternative for a system described by inequalities, equalities and a set inclusion, which are generalizations of Tucker’s classical theorem of the alternative, and develop Kuhn–Tucker necessaryconditions for efficiency to mathematical programs in normed linear spaces involving inequality, equality and set constraints with positive Lagrange multipliers of all the components of objective functions

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  • Bài báo/Newspaper

  • Authors: Dennis Aigner (1977)

  • Previous studies of the so-called frontier production function have not utilized an adequate characterization of the disturbance term for such a model. In this paper we provide an ap propriate specification, by defining the disturbance term as the sum of symmetric normal and (negative) half-normal random variables. Various aspects of maximum-likelihood estimation for the coefficients of a production function with an additive disturbance term of this sort are then considered.

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  • Bài báo/Newspaper

  • Authors: W.W. Cooper (1996)

  • The extensions, new developments and new interpretations for DEA covered in this paper include: (1) new measures of efficiency, (2) new models and (3) new ways of implement ing established models with new results and interpretations presented that include treat ments of "congestion", "returns-to-scale" and "mix" and "technical" inefficiencies and measures of efficiency that can be used to reflect all pertinent properties. Previously used models, such as those used to identify "allocative inefficiencies", are extended by means of "assurance region" approaches which are less demanding in their information require ments and underlying assumptions. New opportunities for research a...

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  • Bài báo/Newspaper

  • Authors: Allen N. Berger (1993)

  • Both input and output inefficiencies are derived from a profit function for US banks. These inefficiencies are decomposed into allocative and technical components in a new way using shadow prices. About half of all potential variable prolits are estimated to be lost to inefliciency. Most inefficiencies are from deficient output revenues, rather than excessive input costs. Larger banks are found to be more efficient than smaller banks, which may offset scale diseconomies found elsewhere. Tests of a new concept, ‘optimal scope economies’, suggest that joint production is optimal for most banks, but that specialization is optimal for others.

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  • Bài báo/Newspaper

  • Authors: R.D. Banker (1996)

  • This brief note adds computational convenience and efficiency to the article by Banker and Thrall on returns to scale in DEA by modifying one of their suggestions to avoid the need for examining all alternate optima in order to reach a decision.

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  • Bài báo/Newspaper

  • Authors: G. E. Battese (1959)

  • A stochastic frontier production function is defined for panel data on firms, in which the non-negative technical inetGciency effects are assumed to be a function of firm-specific variables and time. The inefficiency effects are assumed to be independently distributed as truncations of normal distributions with constant variance, but with means which are a linear function of observ able variables. This panel data model is an extension of recently proposed models for inefTiciency effects in stochastic frontiers for cross-sectional data. An empirical application of the model is obtained using up to ten years of data on paddy farmers from an Indian village. The null hypo theses, that the...