Topic
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: A branch and bound algorithm is presented that globally minimizes a concave cost function over a single convex nonlinear performance constraint and lower and upper bounds on the discrete capacity variables.
22 citations
TL;DR: In this article, the authors prove a duality theorem about the norm of monotonic rearrangements of Bellman functions and show that the norm is a special class of martingales and an extremal problem on this class, which is dual to the minimization problem for locally concave functions.
22 citations
TL;DR: In this paper, exact number of solutions are obtained for a class of two-point boundary value problems involving concave and convex nonlinearities, and some properties of the solutions are studied in details.
Abstract: In this paper, exact number of solutions are obtained for a class of two-point boundary value problems involving concave and convex nonlinearities. Moreover, some properties of the solutions are studied in details.
22 citations
07 Aug 2002
TL;DR: A fluid-stochastic-event graph model is proposed that is a decision-free Petri net that determines continuous-state variables at epochs of failure/repair events and an optimization problem of maximizing a concave function of throughput rate and system parameters is addressed.
Abstract: This paper addresses the performance evaluation and optimization of failure-prone discrete-event systems. We propose a fluid-stochastic-event graph model that is a decision-free Petri net. Tokens are considered as continuous flows. A transition can be in operating state or in failure state. Jumps between failure and operating states do not depend on the firing conditions, and the sojourn time in each state is a random variable of general distribution. For performance evaluation, a set of evolution equations that determines continuous-state variables at epochs of failure/repair events is established. The cumulative firing quantity of each transition is proven to be concave in system parameters, including firing rates and initial marking. Gradient estimators are derived. Finally, an optimization problem of maximizing a concave function of throughput rate and system parameters is addressed.
22 citations
TL;DR: In this paper, the Meyer-Konig and Zeller max-product type operator is introduced and the question of the approximation order by this operator is raised and several shape preserving properties are obtained including the preservation of quasi-convexity.
Abstract: Starting from the study of the Shepard nonlinear operator of max-prod type in [2, 3; 6, Open Problem 5.5.4], the Meyer–Konig and Zeller max-product type operator is introduced and the question of the approximation order by this operator is raised. The first aim of this article is to obtain the order of pointwise approximation for these operators. Also, we prove by a counterexample that in some sense, in general this type of order of approximation with respect to ω1(f; ·) cannot be improved. However, for some subclasses of functions, including for example the continuous nondecreasing concave functions, the essentially better order (of uniform approximation) ω1(f; 1/n) is obtained. Several shape preserving properties are obtained including the preservation of quasi-convexity.
21 citations