Concave function

About: Concave function is a research topic. Over the lifetime, 1415 publications have been published within this topic receiving 33278 citations.

Empirical analysis and simulation of the concave growth pattern of traffic oscillations

Abstract: This paper has investigated the growth pattern of traffic oscillations in the NGSIM vehicle trajectories data, via measuring the standard deviation of vehicle velocity involved in oscillations. We found that the standard deviation of the velocity increases in a concave way along vehicles in the oscillations. Moreover, all datasets collapse into a single concave curve, which indicates a universal evolution law of oscillations. A comparison with traffic experiment shows that the empirical and the experimental results are highly compatible and can be fitted by a single concave curve, which demonstrates that qualitatively the growth pattern of oscillations is not affected by type of bottleneck and lane changing behavior. We have shown theoretically that small disturbance with an angular frequency ω increases in a convex way in the initial stage in the traditional models presuming a unique relationship between speed and density, which obviously deviates from our findings. Simulations show that stochastic models in which the traffic state dynamically spans a 2D region in the speed-spacing plane can qualitatively or even quantitatively reproduce the concave growth pattern of traffic oscillations.

Dynamic Optimization and Learning for Renewal Systems

Abstract: We consider the problem of optimizing time averages in systems with independent and identically distributed behavior over renewal frames. This includes scheduling and task processing to maximize utility in stochastic networks with variable length scheduling modes. Every frame, a new policy is implemented that affects the frame size and that creates a vector of attributes. An algorithm is developed for choosing policies on each frame in order to maximize a concave function of the time average attribute vector, subject to additional time average constraints. The algorithm is based on Lyapunov optimization concepts and involves minimizing a ``drift-plus-penalty'' ratio over each frame. The algorithm can learn efficient behavior without a-priori statistical knowledge by sampling from the past. Our framework is applicable to a large class of problems, including Markov decision problems.

Convex and concave functions of singular values of matrix sums.

Abstract: when / is an increasing concave function of a nonnegative real variable, with /(0) = 0. This inequality is of some interest as in previously published work a convexity (rather than concavity) hypothesis has usually been necessary to establish results of the general type of (1). See, for example, Gohberg and Krein [3], page 49, or Marcus and Mine [4], pages 103 and 116. In this paper we shall uncover the algebraic foundation of (1) by giving a short proof of a generalization. Our proof, which is simpler and more direct than the proof of (1) given by RotfeΓd, will be based on an interesting matrix valued triangle inequality, a special case of which was given by RotfeΓd. We note that the methods used by RotfeΓd are very much adapted to the inequality (1) that he wished to prove, and do not appear capable of proving the extensions of his results to be presented below.

Interactive multiple goal programming

Abstract: Interactive Multiple Goal Programming (IMGP) starts frcm the assumption that the decision maker has defined a number of goal variables g1(x), …, 9m(x), these being concave functions of the instrumental variables x1, …, xn (x in vector notation).

Unitary orbits of Hermitian operators with convex or concave functions

Abstract: This short but self-contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen, sub or super-additivity type inequalities are considered. Some of them are substitutes to classical inequalities (Choi, Davis, Hansen-Pedersen) for operator convex or concave functions. Various trace, norm and determinantal inequalities are derived. Combined with an interesting decomposition for positive semi-definite matrices, several results for partitioned matrices are also obtained.