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Concave function
About: Concave function is a research topic. Over the lifetime, 1415 publications have been published within this topic receiving 33278 citations.
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TL;DR: In this article, the authors define criteria that indicate whether or not an experiment will lead to estimates with distributions well approximated by a normal distribution, based on the intrinsic and parameter effects curvatures.
17 citations
TL;DR: In this article, the authors introduce the notion of a self-concordant convexconcave function, establish basic properties of these functions and develop a path-following interior point method for approximating saddle points of "sufficiently well-behaved" convex concave functions.
Abstract: In this paper, we introduce the notion of a self-concordant convex-concave function, establish basic properties of these functions and develop a path-following interior point method for approximating saddle points of “sufficiently well-behaved” convex-concave functions—those which admit natural self-concordant convex-concave regularizations. The approach is illustrated by its applications to developing an exterior penalty polynomial time method for Semidefinite Programming and to the problem of inscribing the largest volume ellipsoid into a given polytope.
17 citations
TL;DR: In this article, the authors propose a new method for making the inventory replenishment decisions in distribution systems, which is based on formulating the distribution problem as a dynamic program, and relaxing the constraints that ensure the nonnegativity of the shipments to the retailers, by associating Lagrange multipliers with them.
Abstract: We propose a new method for making the inventory replenishment decisions in distribution systems. In particular, we consider distribution systems consisting of multiple retailers that face random demand and a warehouse that supplies the retailers. The method that we propose is based on formulating the distribution problem as a dynamic program, and relaxing the constraints that ensure the nonnegativity of the shipments to the retailers, by associating Lagrange multipliers with them. We show that our method provides lower bounds on the value functions, and a good set of values for the Lagrange multipliers can be obtained by maximizing a concave function in a relatively straightforward manner. Computational experiments indicate that our method can provide significant improvements over the traditional approaches for making the inventory replenishment decisions, in terms of both the tightness of the lower bounds on the value functions and the performance of the policies. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 55: 612-631, 2008
17 citations
TL;DR: In an expected utility analysis of a decision problem, knowledge of the utility function at a few selected points may be available and sufficient conditions for stochastic orderings are presented for the following cases of partially specified utility functions: nondecreasing functions, and nondECreasing concave functions.
Abstract: In an expected utility analysis of a decision problem, knowledge of the utility function at a few selected points may be available. When combined with general properties such as monotonicity or concavity, the limited knowledge of the utility function may be sufficient for ranking a pair of probability distributions unambiguously. Necessary and sufficient conditions for such stochastic orderings are presented for the following cases of partially specified utility functions: nondecreasing functions, and nondecreasing concave functions. Examples of these orderings are presented.
17 citations
TL;DR: These results are mainly based on the Brunn–Minkowski Theorem and a theorem of Keith Ball, which allow us to reduce to a 2-dimensional version of the problem.
Abstract: elements of some (finite) poset , write for the probability that precedes in a random (uniform) linear extension of For define where the infimum is over all choices of and distinct Addressing an issue raised by Fishburn [6], we give the first nontrivial lower bounds on the function This is part of a more general geometric result, the exact determination of the function where the infimum is over chosen uniformly from some compact convex subset of a Euclidean space These results are mainly based on the Brunn–Minkowski Theorem and a theorem of Keith Ball [1], which allow us to reduce to a 2-dimensional version of the problem
17 citations