Stochastic Block Mirror Descent Methods for Nonsmooth and Stochastic Optimization

In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the block-coordinate decomposition and an incremental block averaging scheme into the classic (stochastic) mirror-descent method, in order to significantly reduce the cost per iteration of the latter algorithm. We establish the rate of convergence of the SBMD method along with its associated large-deviation results for solving general nonsmooth and stochastic optimization problems. We also introduce different variants of this method and establish their rate of convergence for solving strongly convex, smooth, and composite optimization problems, as well as certain nonconvex optimization problems. To the best of our knowledge, all these developments related to the SBMD methods are new in the stochastic optimization literature. Moreover, some of our results also seem to be new for block coordinate descent methods for deterministic optimization

Linearly Convergent First-Order Algorithms for Semi-definite Programming

In this paper, we consider two formulations for Linear Matrix Inequalities (LMIs) under Slater type constraint qualification assumption, namely, SDP smooth and non-smooth formulations. We also propose two first-order linearly convergent algorithms for solving these formulations. Moreover, we introduce a bundle-level method which converges linearly uniformly for both smooth and non-smooth problems and does not require any smoothness information. The convergence properties of these algorithms are also discussed. Finally, we consider a special case of LMIs, linear system of inequalities, and show that a linearly convergent algorithm can be obtained under a weaker assumption

Constraints on the Dark Side of the Universe and Observational Hubble Parameter Data

This paper is a review on the observational Hubble parameter data that have gained increasing attention in recent years for their illuminating power on the dark side of the universe --- the dark matter, dark energy, and the dark age. Currently, there are two major methods of independent observational H(z) measurement, which we summarize as the "differential age method" and the "radial BAO size method". Starting with fundamental cosmological notions such as the spacetime coordinates in an expanding universe, we present the basic principles behind the two methods. We further review the two methods in greater detail, including the source of errors. We show how the observational H(z) data presents itself as a useful tool in the study of cosmological models and parameter constraint, and we also discuss several issues associated with their applications. Finally, we point the reader to a future prospect of upcoming observation programs that will lead to some major improvements in the quality of observational H(z) data.Comment: 20 pages, 6 figures, and 1 table, uses REVTeX 4.1. Review article, accepted by Advances in Astronom

Computation of transient viscous flows using indirect radial basis function networks

In this paper, an indirect/integrated radial-basis-function network (IRBFN) method is further developed to solve transient partial differential equations (PDEs) governing fluid flow problems. Spatial derivatives are discretized using one- and two-dimensional IRBFN interpolation schemes, whereas temporal derivatives are approximated using a method of lines and a finite-difference technique. In the case of moving interface problems, the IRBFN method is combined with the level set method to capture the evolution of the interface. The accuracy of the method is investigated by considering several benchmark test problems, including the classical lid-driven cavity flow. Very accurate results are achieved using relatively low numbers of data points

Implementation of UAV Coordination Based on a Hierarchical Multi-UAV Simulation Platform

In this paper, a hierarchical multi-UAV simulation platform,called XTDrone, is designed for UAV swarms, which is completely open-source 4 . There are six layers in XTDrone: communication, simulator,low-level control, high-level control, coordination, and human interac-tion layers. XTDrone has three advantages. Firstly, the simulation speedcan be adjusted to match the computer performance, based on the lock-step mode. Thus, the simulations can be conducted on a work stationor on a personal laptop, for different purposes. Secondly, a simplifiedsimulator is also developed which enables quick algorithm designing sothat the approximated behavior of UAV swarms can be observed inadvance. Thirdly, XTDrone is based on ROS, Gazebo, and PX4, andhence the codes in simulations can be easily transplanted to embeddedsystems. Note that XTDrone can support various types of multi-UAVmissions, and we provide two important demos in this paper: one is aground-station-based multi-UAV cooperative search, and the other is adistributed UAV formation flight, including consensus-based formationcontrol, task assignment, and obstacle avoidance.Comment: 12 pages, 10 figures. And for the, see https://gitee.com/robin_shaun/XTDron

Integrating Managerial Pattern and Competitive Advantages: The Moderation of Competitive Inertia

In dynamic competition, the competitive inertia is determined by components both inside and outside of company. This paper investigated that, after integration, how can firm appropriately alter their integrating managerial pattern, according to competitive inertia, in order to achieve better advantages cause from integration. Through 10-year data of the oligopoly enterprises in airconditioner industry in China, the analysis demonstrated that, improving flexibilities of integration managerial pattern helps to build differentiation advantages, while negative to cost advantages; while firm competitive inertia grew, systematicness of integration managerial pattern would have positive effects on differentiation advantages, while negative on cost advantages.Key words: Integrating managerial pattern; Competitive dynamics; Competitive inertia; Competitive advantage