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: This paper proposes an alternative to nonparametric segmented concave least squares by using a differentiable approximation to an arbitrary functional form based on smoothly mixing Cobb-Douglas anchor functions over the data space.
9 citations
TL;DR: In this paper, a characterization of risk functions of Stein-type estimators is obtained by using an apparently little known fact about concave functions together with a new expectation identity for noncentral chi-squared random variables.
9 citations
01 Sep 2008
9 citations
TL;DR: This work considers a cumulative scheduling problem where a task duration and resource consumption are not fixed and presents two propagation algorithms that combine a flow-based checker with time-bound adjustments derived from the time-table disjunctive reasoning for the cumulative constraint.
Abstract: We consider a cumulative scheduling problem where a task duration and resource consumption are not fixed The consumption profile of the task, which can vary continuously over time, is a decision variable of the problem to be determined and a task is completed as soon as the integration over its time window of a non-decreasing and continuous processing rate function of the consumption profile has reached a predefined amount of energy The goal is to find a feasible schedule, which is an NP-hard problem For the case where functions are concave and piecewise linear, we present two propagation algorithms The first one is the adaptation to concave functions of the variant of the energetic reasoning previously established for linear functions Furthermore, a full characterization of the relevant intervals for time-window adjustments is provided The second algorithm combines a flow-based checker with time-bound adjustments derived from the timetable disjunctive reasoning for the cumulative constraint Complementarity of the algorithms is assessed via their integration in a hybrid branch-and-bound and computational experiments on small-size instances
9 citations
TL;DR: In this article, a modified Piyavskii's algorithm (nC) was proposed to maximize a univariate differentiable function by iteratively constructing an upper bound of a piece-wise concave function of f and evaluating f at a point where Φ reaches its maximum.
Abstract: Piyavskii’s algorithm maximizes a univariate function satisfying a Lipschitz condition. We propose a modified Piyavskii’s sequential algorithm which maximizes a univariate differentiable function f by iteratively constructing an upper bounding piece-wise concave function Φ of f and evaluating f at a point where Φ reaches its maximum. We compare the numbers of iterations needed by the modified Piyavskii’s algorithm (nC) to obtain a bounding piece-wise concave function Φ whose maximum is within e of the globally optimal value foptwith that required by the reference sequential algorithm (nref). The main result is that nC≤ 2nref + 1 and this bound is sharp. We also show that the number of iterations needed by modified Piyavskii’s algorithm to obtain a globally e-optimal value together with a corresponding point (nB) satisfies nBnref + 1 Lower and upper bounds for nref are obtained as functions of f(x) , e, M1 and M0 where M0 is a constant defined by M0 = supx∈[a,b] - f’’(x) and M1 ≥ M0 is an evaluation of M0.
9 citations