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In this paper, we present a new conditional gradient type method for convex optimization by calling a linear optimization (LO) oracle to minimize a series of linear functions over the feasible set. Different from the classic conditional gradient method, the conditional gradient sliding (CGS) algorithm developed herein can skip the computation of gradients from time to time and, as a result, can achieve the optimal complexity bounds in terms of not only the number of calls to the LO oracle but also the number of gradient evaluations. More specifically, we show that the CGS method requires O(1/ √ ) and O(log(1/ )) gradient evaluations, respectively, for solving smooth and strongly convex problems, while still maintaining the optimal O(1/ ) bound on the number of calls to the LO oracle. We also develop variants of the CGS method which can achieve the optimal complexity bounds for solving stochastic optimization problems and an important class of saddle point optimization problems. To the best of our knowledge, this is the first time that these types of projection-free optimal first-order methods have been developed in the literature. Some preliminary numerical results have also been provided to demonstrate the advantages of the CGS method.

In this paper, we consider a class of finite-sum convex optimization problems whose objective function is given by the summation of m (≥ 1) smooth components together with some other relatively simple terms. We first introduce a deterministic primal-dual gradient (PDG) method that can achieve the optimal blackbox iteration complexity for solving these composite optimization problems using a primal-dual termination criterion. Our major contribution is to develop a randomized primal-dual gradient (RPDG) method, which needs to compute the gradient of only one randomly selected smooth component at each iteration, but can possibly achieve better complexity than PDG in terms of the total number of gradient evaluations. More specifically, we show that the total number of gradient evaluations performed by RPDG can be O( √ m) times smaller, both in expectation and with high probability, than those performed by deterministic optimal first-order methods under favorable situations. We also show that the complexity of the RPDG method is not improvable by developing a new lower complexity bound for a general class of randomized methods for solving large-scale finite-sum convex optimization problems. Moreover, through the development of PDG and RPDG, we introduce a novel gametheoretic interpretation for these optimal methods for convex optimization.

We present a new class of decentralized first-order methods for nonsmooth and stochastic optimization problems defined over multiagent networks. Considering that communication is a major bottleneck in decentralized optimization, our main goal in this paper is to develop algorithmic frameworks which can significantly reduce the number of inter-node communications. We first propose a decentralized primal-dual method which can find an ǫ-solution both in terms of functional optimality gap and feasibility residual in O(1/ǫ) inter-node communication rounds when the objective functions are convex and the local primal subproblems are solved exactly. Our major contribution is to present a new class of decentralized primal-dual type algorithms, namely the decentralized communication sliding (DCS) methods, which can skip the inter-node communications while agents solve the primal subproblems iteratively through linearizations of their local objective functions. By employing DCS, agents can still find an ǫ-solution in O(1/ǫ) (resp., O(1/ √ ǫ)) communication rounds for general convex functions (resp., strongly convex functions), while maintaining the O(1/ǫ 2 ) (resp., O(1/ǫ)) bound on the total number of intra-node subgradient evaluations. We also present a stochastic counterpart for these algorithms, denoted by SDCS, for solving stochastic optimization problems whose objective function cannot be evaluated exactly. In comparison with existing results for decentralized nonsmooth and stochastic optimization, we can reduce the total number of inter-node communication rounds by orders of magnitude while still maintaining the optimal complexity bounds on intra-node stochastic subgradient evaluations. The bounds on the (stochastic) subgradient evaluations are actually comparable to those required for centralized nonsmooth and stochastic optimization under certain conditions on the target accuracy.Address(es) of author(s) should be given √ ǫ)) communication rounds while maintaining the O(1/ǫ 2 ) (resp., O(1/ǫ)) bound on the total number of intra-node subgradient evaluations when the objective functions are general convex (resp., strongly convex). The bounds on the subgradient evaluations are actually comparable to those optimal complexity bounds required for centralized nonsmooth optimization under certain conditions on the target accuracy, and hence are not improvable in general.Thirdly, we present a stochastic decentralized communication sliding method, denoted by SDCS, for solving stochastic optimization problems and show complexity bounds similar to those of DCS on the total number of required communication rounds and stochastic subgradient evaluations. In particular, only O(1/ǫ) (resp., O(1/ √ ǫ))

Analysis of Internet of Things (IoT) sensor data is a key for achieving city smartness. In this paper a multitier fog computing model with large-scale data analytics service is proposed for smart cities applications. The multi-tier fog is consisted of ad-hoc fogs and dedicated fogs with opportunistic and dedicated computing resources, respectively. The proposed new fog computing model with clear functional modules is able to mitigate the potential problems of dedicated computing infrastructure and slow response in cloud computing. We run analytics benchmark experiments over fogs formed by Rapsberry Pi computers with a distributed computing engine to measure computing performance of various analytics tasks, and create easy-to-use workload models. QoS aware admission control, offloading and resource allocation schemes are designed to support data analytics services, and maximize analytics service utilities. Availability and cost models of networking and computing resources are taken into account in QoS scheme design. A scalable system level simulator is developed to evaluate the fog based analytics service and the QoS management schemes. Experiment results demonstrate the efficiency of analytics services over multi-tier fogs and the effectiveness of the proposed QoS schemes. Fogs can largely improve the performance of smart city analytics services than cloud only model in terms of job blocking probability and service utility.

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Object detection is a critical problem for advanced driving assistance systems (ADAS). Recently convolutional neural networks (CNN) achieved large successes on object detection, with performance improvement over traditional approaches, which use hand-engineered features. However, due to the challenging driving environment (e.g., large object scale variation, object occlusion and bad light conditions), popular CNN detectors do not achieve very good object detection accuracy over the KITTI autonomous driving benchmark dataset. In this paper we propose three enhancements for CNN based visual object detection for ADAS. To address the large object scale variation challenge, deconvolution and fusion of CNN feature maps are proposed to add context and deeper features for better object detection at low feature map scales. In addition, soft non-maximal suppression (NMS) is applied across object proposals at different feature scales to address the object occlusion challenge. As the cars and pedestrians have distinct aspect ratio features, we measure their aspect ratio statistics and exploit them to set anchor boxes properly for better object matching and localization. The proposed CNN enhancements are evaluated with various image input sizes by experiments over KITTI dataset. Experiment results demonstrate the effectiveness of the proposed enhancements with good detection performance over KITTI test set.