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Efficient auctions for distributed transportation procurement

TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2014年 65卷 47-64页

作者： Xu, Su Xiu Huang, George Q. Univ Hong Kong HKU ZIRI Lab Phys Internet Dept Ind & Mfg Syst Engn Hong Kong Hong Kong Peoples R China

The purpose of this paper is to propose allocatively efficient auction mechanisms for the distributed transportation procurement problem (DTPP), which is generally the problem of matching demands and supplies over a transportation network. We first construct a one-sided Vickrey-Clarke-Groves (O-VCG) combinatorial auction for the DTPP where carriers are allowed to bid on bundles of lanes. The O-VCG auction minimizes the total transportation cost (i.e., allocative efficiency) and induces truthful bidding from carriers (i.e., incentive compatibility). To simplify the execution of auction, we next propose a primal-dual Vickrey (PDV) auction based on insights from the known Ausubel auctions and the primal-dual algorithm. The PDV auction is actually a multi-round descending auction that seems simple enough for bidders. The PDV auction realizes VCG payments and truthful bidding under the condition of seller-submodularity, which implies that the effect of each individual carrier is decreasing when the coalition increases. Such is the case for the DTPP in an oversupplied transportation market. The winner determination problem of O-VCG auction is solved by the proposed primal-dual algorithm when seller-submodularity holds. Finally, carriers may reveal less private information in the PDV auction due to its dynamic procedures. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Distributed transportation procurement Mechanism design Efficient auctions primal-dual algorithm Incentive compatibility

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Reducing Artifacts in JPEG Decompression Via a Learned Dictionary

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2014年第3期62卷 718-728页

作者： Chang, Huibin Ng, Michael K. Zeng, Tieyong Tianjin Normal Univ Sch Math Sci Tianjin 300387 Peoples R China Hong Kong Baptist Univ Dept Math Ctr Math Imaging & Vis Kowloon Tong Hong Kong Peoples R China

The JPEG compression method is among the most successful compression schemes since it readily provides good compressed results at a rather high compression ratio. However, the decompressed result of the standard JPEG decompression scheme usually contains some visible artifacts, such as blocking artifacts and Gibbs artifacts (ringing), especially when the compression ratio is rather high. In this paper, a novel artifact reducing approach for the JPEG decompression is proposed via sparse and redundant representations over a learned dictionary. Indeed, an effective two-step algorithm is developed. The first step involves dictionary learning and the second step involves the total variation regularization for decompressed images. Numerical experiments are performed to demonstrate that the proposed method outperforms the total variation and weighted total variation decompression methods in the measure of peak of signal to noise ratio, and structural similarity.

关键词： JPEG decompression total variation learned dictionary primal-dual algorithm

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Inertial Douglas-Rachford splitting for monotone inclusion problems

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APPLIED MATHEMATICS AND COMPUTATION 2015年 256卷 472-487页

作者： Bot, Radu Ioan Csetnek, Ernoe Robert Hendrich, Christopher Univ Vienna Fac Math A-1090 Vienna Austria Tech Univ Chemnitz Dept Math D-09107 Chemnitz Germany

We propose an inertial Douglas-Rachford splitting algorithm for finding the set of zeros of the sum of two maximally monotone operators in Hilbert spaces and investigate its convergence properties. To this end we formulate first the inertial version of the Krasnosel'skii-Mann algorithm for approximating the set of fixed points of a nonexpansive operator, for which we also provide an exhaustive convergence analysis. By using a product space approach we employ these results to the solving of monotone inclusion problems involving linearly composed and parallel-sum type operators and provide in this way iterative schemes where each of the maximally monotone mappings is accessed separately via its resolvent. We consider also the special instance of solving a primal-dual pair of nonsmooth convex optimization problems and illustrate the theoretical results via some numerical experiments in clustering and location theory. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Inertial splitting algorithm Douglas-Rachford splitting Krasnosel'skii-Mann algorithm primal-dual algorithm Convex optimization

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Sparse Hierarchical Interaction Learning with Epigraphical Projection

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JOURNAL OF SIGNAL PROCESSING SYSTEMS FOR SIGNAL IMAGE AND VIDEO TECHNOLOGY 2020年第7期92卷 637-654页

作者： Jiu, Mingyuan Pustelnik, Nelly Janaqi, Stefan Chebre, Meriam Qi, Lin Ricoux, Philippe Zhengzhou Univ Sch Informat Engn Zhengzhou 450001 Peoples R China Univ Lyon Lab Phys CNRS Ens LyonUniv Lyon 1 F-69342 Lyon France TOTAL SA Direct Sci F-92069 Paris France

This work focuses on learning optimization problems with quadratical interactions between variables, which go beyond the additive models of traditional linear learning. We investigate more specifically two different methods encountered in the literature to deal with this problem: "hierNet" and structured-sparsity regularization, and study their connections. We propose a primal-dual proximal algorithm based on an epigraphical projection to optimize a general formulation of these learning problems. The experimental setting first highlights the improvement of the proposed procedure compared to state-of-the-art methods based on fast iterative shrinkage-thresholding algorithm (i.e. FISTA) or alternating direction method of multipliers (i.e. ADMM), and then, using the proposed flexible optimization framework, we provide fair comparisons between the different hierarchical penalizations and their improvement over the standard l(1)-norm penalization. The experiments are conducted both on synthetic and real data, and they clearly show that the proposed primal-dual proximal algorithm based on epigraphical projection is efficient and effective to solve and investigate the problem of hierarchical interaction learning.

关键词： Regression learning Multiclass SVMs Hierarchical interaction primal-dual algorithm Epigraphical projection

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Distributed Event-Triggered Communication Scheme for Economic Dispatch Problem in Power System With Uncoordinated Step-Sizes

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IEEE ACCESS 2020年 8卷 43466-43475页

作者： Feng, Yuming Zhang, Wei Xiong, Jiang Li, Huaqing Chongqing Three Gorges Univ Key Lab Intelligent Informat Proc & Control Chongqing 404100 Peoples R China Southwest Univ Chongqing Key Lab Nonlinear Circuits & Intelligen Coll Elect & Informat Engn Chongqing 400715 Peoples R China

Inspired by the distributed economic dispatch problem (EDP) in power system, this paper considers a problem of optimizing a sum of m local convex cost functions on an undirected network of m agents. Each agent in the network privately knows its own local convex objective function and is subjected to both coupling linear constraint and individual box constraints. To be able to reduce the requirements for information exchange among agents, we propose a novel fully event-triggered based distributed primal-dual algorithm for the convex optimization problem. Our algorithm allows the use of uncoordinated step-sizes and assumes that each agent communicates with its neighboring agents (the corresponding variables are updated) only at some independent event-triggered sampling time instants. Under some relatively standard assumptions (strong convexity and smoothness) on the objective functions, our theoretical analysis proves that the proposed algorithm can linearly seek the exact optimal solution when the upper bound of the uncoordinated step-sizes is smaller than a certain constant. We also conduct a clear estimate of the rate. Finally, a simple numerical example on distributed economic dispatch problem in power system is provided to illustrate the effectiveness of our event-triggered based optimization algorithm and validate the correctness of the analysis process.

关键词： Distributed convex optimization event-triggered scheme primal-dual algorithm linear convergence rate power system

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Color Transfer Using Adaptive Second-Order Total Generalized Variation Regularizer

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IEEE ACCESS 2018年 6卷 6829-6839页

作者： Xie, Bin Xu, Chen Han, Yu Teng, Robert K. F. Shenzhen Univ Coll Informat Engn Shenzhen 518060 Peoples R China Jiangxi Univ Sci & Technol Coll Informat Engn Ganzhou 341000 Peoples R China Shenzhen Univ Coll Math & Stat Shenzhen 518060 Peoples R China

Color transfer is to generate synthetic images by changing the color of target images with new colors obtained from given source images, while the geometrical structure of the synthetic images remains the same. Classical color transfer models use a total variation (TV) regularizer to preserve the details and suppress the noise of the synthetic images. These models can sometimes cause staircase effect and geometrical structure details over-smoothed. To overcome these problems, we propose a new color transfer model in which an adaptive second-order total generalized variation (TGV) regularizer is designed. Here, the adaptive second-order TGV regularizer is a weighted second-order TGV regularizer. The weight is computed by an adaptive edge indicator function. In addition, an efficient algorithm is developed to program our new model. The algorithm is based on a weighted primal-dual method. Experimental results and comparisons demonstrate that our new color transfer model can generate better results than classical TV regularizer-based models in the aspects of the inhibition of staircase effect and the preservation of image details.

关键词： Color transfer staircase effect total variation (TV) total generalized variation (TGV) primal-dual algorithm

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An online stochastic algorithm for a dynamic nurse scheduling problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第1期285卷 196-210页

作者： Legrain, Antoine Omer, Jeremy Rosat, Samuel Polytech Montreal 2900 Blvd Edouard MontpetitCampus Univ Montreal Montreal PQ H3T 1J4 Canada Univ Montreal Interuniv Res Ctr Enterprise Networks Logist & Tr Pavillon Andre AisenstadtCP 6128 Montreal PQ H3C 3J7 Canada Univ Rennes CNRS INSA Rennes IRMARUMR 6625 F-35000 Rennes France HEC Montreal Grp Res Decis Anal GERAD 3000 Ch Cote St Catherine Montreal PQ H3T 2A7 Canada

In this paper, we focus on the problem studied in the second international nurse rostering competition: a personalized nurse scheduling problem under uncertainty. The schedules must be computed week by week over a planning horizon of up to eight weeks. We present the work that the authors submitted to this competition and which was awarded the second prize. At each stage, the dynamic algorithm is fed with the staffing demand and nurses preferences for the current week and computes an irrevocable schedule for all nurses without knowledge of future inputs. The challenge is to obtain a feasible and near-optimal schedule at the end of the horizon. The online stochastic algorithm described in this paper draws inspiration from the primal-dual algorithm for online optimization and the sample average approximation, and is built upon an existing static nurse scheduling software. The procedure generates a small set of candidate schedules, rank them according to their performance over a set of test scenarios, and keeps the best one. Numerical results show that this algorithm is very robust, since it has been able to produce feasible and near optimal solutions on most of the proposed instances ranging from 30 to 120 nurses over a horizon of 4 or 8 weeks. Finally, the code of our implementation is open source and available in a public repository. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Stochastic programming Nurse rostering Dynamic problem Sample average approximation primal-dual algorithm Scheduling

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SOLVING COUPLED COMPOSITE MONOTONE INCLUSIONS BY SUCCESSIVE FEJER APPROXIMATIONS OF THEIR KUHN-TUCKER SET

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SIAM JOURNAL ON OPTIMIZATION 2014年第4期24卷 2076-2095页

作者： Alotaibi, Abdullah Combettes, Patrick L. Shahzad, Naseer King Abdulaziz Univ Dept Math Jeddah 21859 Saudi Arabia Univ Paris 06 Sorbonne Univ UMR 7598 Lab Jacques Louis Lions F-75005 Paris France

We propose a new class of primal-dual Fejer monotone algorithms for solving systems of composite monotone inclusions. Our construction is inspired by a framework used by Eckstein and Svaiter for the basic problem of finding a zero of the sum of two monotone operators. At each iteration, points in the graph of the monotone operators present in the model are used to construct a half-space containing the Kuhn-Tucker set associated with the system. The primal-dual update is then obtained via a relaxed projection of the current iterate onto this half-space. An important feature that distinguishes the resulting splitting algorithms from existing ones is that they do not require prior knowledge of bounds on the linear operators involved or the inversion of linear operators.

关键词： duality Fejer monotonicity monotone inclusion monotone operator primal-dual algorithm splitting algorithm

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Structure-Oriented DTGV Regularization for Random Noise Attenuation in Seismic Data

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2021年第2期59卷 1757-1771页

作者： Wang, Dehua Gao, Jinghuai Liu, Naihao Jiang, Xiudi Xian Technol Univ Sch Sci Xian 710021 Peoples R China Univ Elect Sci & Technol China Sch Math Sci Chengdu 611731 Peoples R China Xi An Jiao Tong Univ Sch Informat & Commun Engn Xian 710049 Peoples R China Natl Engn Lab Offshore Oil Explorat Xian 710049 Peoples R China China Natl Offshore Oil Corp CNOOC Res Inst Technol Res & Dev Ctr Geophys Key Lab Beijing 100029 Peoples R China

Noise attenuation is a very important step in seismic data processing, which facilitates accurate geologic interpretation. Random noise is one of the main factors that lead to reductions in the signal-to-noise ratio (SNR) of seismic data. It is necessary for seismic data, including complex geological structures, to develop a number of new noise attenuation technologies. In this article, we concern with a new variational regularization method for random noise attenuation of seismic data. Considering that seismic reflection events often have spatially varying directions, we first employ the gradient structure tensor (GST) to estimate the spatially varying dips point by point and propose the structure-oriented directional total generalized variation (DTGV) (SODTGV) functional. Then, we employ the SODTGV as a regularizer to establish an $\ell _{2}$ -SODTGV model and develop the primal-dual algorithm for solving this model. Next, the choice of the model parameters is discussed. Finally, the proposed model is applied to restore noisy synthetic and field data to verify the effectiveness of the proposed workflow. For contrastive methods, we select the structure adaptive median filtering (SAMF), anisotropic total variation (ATV), total generalized variation (TGV), DTGV, median filtering, KL transform, SVD transform, and curvelet transform. The synthetic and real seismic data examples indicate that our proposed method can preferably improve the vertical resolution of seismic profiles, enhance the lateral continuity of reflection events, and preserve local geologic features while improving the SNR. Moreover, the proposed regularization method can also be applied to other inverse problems, such as image processing, medical imaging, and remote sensing.

关键词： TV Attenuation Transforms Oils Geology Data models Signal to noise ratio Gradient structure tensor (GST) Noise attenuation primal-dual algorithm structure-oriented variational regularization

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STOCHASTIC QUASI-FEJER BLOCK-COORDINATE FIXED POINT ITERATIONS WITH RANDOM SWEEPING

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SIAM JOURNAL ON OPTIMIZATION 2015年第2期25卷 1221-1248页

作者： Combettes, Patrick L. Pesquet, Jean-Christophe Univ Paris 06 Sorbonne Univ UMR 7598 Lab Jacques Louis Lions F-75005 Paris France Univ Paris Est CNRS UMR 8049 Lab Informat Gaspard Monge F-77454 Marne La Vallee 2 France

This work proposes block-coordinate fixed point algorithms with applications to nonlinear analysis and optimization in Hilbert spaces. The asymptotic analysis relies on a notion of stochastic quasi-Fejer monotonicity, which is thoroughly investigated. The iterative methods under consideration feature random sweeping rules to select arbitrarily the blocks of variables that are activated over the course of the iterations and they allow for stochastic errors in the evaluation of the operators. algorithms using quasi-nonexpansive operators or compositions of averaged nonexpansive operators are constructed, and weak and strong convergence results are established for the sequences they generate. As a by-product, novel block-coordinate operator splitting methods are obtained for solving structured monotone inclusion and convex minimization problems. In particular, the proposed framework leads to random block-coordinate versions of the Douglas-Rachford and forward-backward algorithms and of some of their variants. In the standard case of m = 1 block, our results remain new as they incorporate stochastic perturbations.

关键词： arbitrary sampling block-coordinate algorithm fixed-point algorithm monotone operator splitting primal-dual algorithm stochastic quasi-Fejer sequence stochastic algorithm structured convex minimization problem

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