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Network utility maximization revisited: Three issues and their resolution

PERFORMANCE EVALUATION 2019年 136卷 102050-000页

作者： Akhil, P. T. Sundaresan, Rajesh Indian Inst Sci Dept Elect Commun Engn Bangalore 560012 Karnataka India Indian Inst Sci Robert Bosch Ctr Cyber Phys Syst Bangalore 560012 Karnataka India

Distributed and iterative network utility maximization algorithms, such as the primal dual algorithms or the network-user decomposition algorithms, often involve trajectories where the iterates may be infeasible, convergence to the optimal points of relaxed problems different from the original, or convergence to local maxima. In this paper, we highlight the three issues with iterative algorithms. We then propose a distributed and iterative algorithm that does not suffer from the three issues. In particular, we assert the feasibility of the algorithm's iterates at all times, convergence to global maximum of the given problem (rather than to global maximum of a relaxed problem), and avoidance of any associated spurious rest points of the dynamics. A benchmark algorithm due to Kelly et al. (1998) involves fast user updates coupled with slow network updates in the form of additive-increase multiplicative-decrease of suggested user flows. The proposed algorithm may be viewed as one with fast user updates and fast network updates that keeps the iterates feasible at all times. Simulations suggest that the convergence rate of the ordinary differential equation (ODE) tracked by our proposed algorithm's iterates is comparable to that of the ODE for the aforementioned benchmark algorithm. (C) 2019 Elsevier B.V. All rights reserved.

关键词： convex programming Network utility maximization Kelly decomposition Distributed interior point method

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A new sampling scheme combining maximum entropy and moment matching techniques for reactor physics uncertainty quantification

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ANNALS OF NUCLEAR ENERGY 2023年第1期187卷

作者： Ji, Bingbing Chen, Zhiping Liu, Jia Zou, Xiaoyang Wan, Chenghui Cao, Liangzhi Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Peoples R China Xian Int Acad Math & Math Technol Ctr Optimizat Tech & Quantitat Finance Xian 710049 Peoples R China Xi An Jiao Tong Univ Sch Nucl Sci & Technol Xian 710049 Peoples R China

The sampling method is widely used for the quantification of reactor physics analysis uncertainty, while the traditional statistical sampling methods often require a huge number of samples to ensure the stability of uncertainty quantification results. For this reason, a new two-step sampling scheme based on the combination of information entropy theory and moment matching technique is proposed for the quantification of the reactor physics uncertainty. We construct a convex programming model to optimize initial samples by simultaneously maximizing information entropy and minimizing moment deviations. The optimized samples can not only characterize the statistics of the real distribution better, but also control the information entropy with a smaller sample size. Moreover, a quantitative criterion for sample selection induced by the maximum entropy and moment matching is proposed. Finally, a series of empirical studies are carried out to show the capability and efficiency of the introduced two-step sampling method.

关键词： Reactor physics analysis Uncertainty quantification Information entropy Moment matching convex programming

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An Interior Point Method Applied to Flow Constraints in a Pressure-Dependent Water Distribution System

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JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT 2022年第1期148卷 04021090-04021090页

作者： Elhay, Sylvan Piller, Olivier Deuerlein, Jochen W. Simpson, Angus R. Univ Adelaide Sch Comp Sci Adelaide SA 5005 Australia INRA Dept Aqua Environm Terr & Infrastruct Res Unit Res Unit 50 Ave Verdun F-33612 Gazinet Cestas France Univ Adelaide Sch Civil Environm & Min Engn Adelaide SA 5005 Australia 3S Consult GmbH Albtalstr 13 D-76137 Karlsruhe Germany

This paper used the fusion of an active-set method (ASM) and an interior point method (IPM), with a Newton method, to solve for the steady-state flows, heads, and outflows of a pressure-dependent water distribution system. The outflow constraints which arise from the pressure dependency are handled by an ASM, and the linkflow constraints are handled by an IPM. The authors believe that this is the first time an ASM and an IPM have been used together in this way to solve a real-world optimization problem. Including flow constraints in a network model allows a variety of flow control devices (flow control valves, check valves, pumps) to be modeled efficiently. The new method does not require damping. The separate treatment methods for the two constraint sets mean that the linear inequality constraint qualification condition cannot be violated during iteration, unlike the case in which all the constraints are handled by an ASM. The method was shown to converge quickly on nine case study networks, the largest of which had more than 157,000 links, 150,000 nodes, and 6,000 linkflow constraints. When tested on those same nine networks, an interior point optimizer software package took about 2-4 times longer than the new method for five of the networks, 7 and 9 times as long for two of the networks, and about an equal amount of time for the remaining two networks. For the largest network, the software package took 34 min, whereas the method presented here took 4 min. The generality of the method makes it applicable to network design and management, capacity analysis, and self-cleaning networks.

关键词： Networks convex programming Interior point methods (IPMs) Active-set methods (ASMs) Flow control

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New convex approaches to general MVDR robust adaptive beamforming problems

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ELECTRONICS LETTERS 2023年第18期59卷 e12957-e12957页

作者： Zhao, Yao Liu, Qingsong Tian, He Luo, Mingfan Ling, Bingo Wing-Kuen Zhang, Zhe Guangdong Univ Technol Guangzhou Peoples R China Natl Key Lab Scattering & Radiat Beijing Peoples R China Beijing Inst Environm Features Beijing Peoples R China Surveying & Mapping Inst Lands & Resource Dept Guangdong Prov Guangzhou Peoples R China Suzhou Key Lab Microwave Imaging Proc & Applicat T Suzhou Peoples R China Suzhou Aerosp Informat Res Inst Suzhou Peoples R China Natl Key Lab Microwave Imaging Technol Beijing Peoples R China Chinese Acad Sci Aerosp Informat Res Inst Beijing Peoples R China

Consider general minimum variance distortionless response (MVDR) robust adaptive beamforming problems based on the optimal estimation for both the desired signal steering vector and the interference-plus-noise covariance (INC) matrix. The optimal robust adaptive beamformer design problem is an array output power maximization problem, subject to three constraints on the steering vector, namely, a (convex or nonconvex) quadratic constraint ensuring that the direction-of-arrival (DOA) of the desired signal is separated from the DOA region of all linear combinations of the interference steering vectors, a double-sided norm constraint, and a similarity constraint;as well as a ball constraint on the INC matrix, which is centered at a given data sample covariance matrix. To tackle the nonconvex problem, a new tightened semidefinite relaxation (SDR) approach is proposed to output a globally optimal solution;otherwise, a sequential convex approximation (SCA) method is established to return a locally optimal solution. The simulation results show that the MVDR robust adaptive beamformers based on the optimal estimation for the steering vector and the INC matrix have better performance (in terms of, e.g., the array output signal-to-interference-plus-noise ratio) than the existing MVDR robust adaptive beamformers by the steering vector estimation only. This paper addresses the general minimum variance distortionless response (MVDR) robust adaptive beamforming problem, focusing on optimal estimations for the desired signal steering vector and the interference-plus-noise covariance (INC) matrix. A new tightened semidefinite relaxation (SDR) method is introduced to provide globally optimal solutions for nonconvex challenges, with a sequential convex approximation method as an alternative for local optimization. Simulations demonstrate that the proposed MVDR beamformers, based on both the steering vector and INC matrix, outperform those relying solely on steering vector estimation.i

关键词： array signal processing convex programming relaxation theory

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Co-Design of CVT-Based Electric Vehicles

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ENERGIES 2021年第7期14卷 1825-1825页

作者： Wei, Caiyang Hofman, Theo Ilhan Caarls, Esin Eindhoven Univ Technol Dept Mech Engn POB 513 NL-5600 MB Eindhoven Netherlands Bosch Transmiss Technol Postbus 500 NL-5000 AM Tilburg Netherlands

For an electric vehicle (EV) with a continuously variable transmission (CVT), a novel convex programming (CP)-based co-design method is proposed to minimize the total-cost-of-ownership (TCO). The integration of the electric machine (EM) and the CVT is the primary focus. The optimized system with co-design reduces the TCO by around 5.9% compared to a non-optimized CVT-based EV (based on off-the-shelf components) and by around 2% compared to the EV equipped with a single-speed transmission (SST). By taking advantage of the control and design freedom provided by the CVT, the optimal CVT, EM and battery sizes are found to reduce the system cost. It simultaneously finds the optimal CVT speed ratio and air-flow rate of the cooling system reducing the energy consumption. The strength of co-design is highlighted by comparing to a sequential design, and insights into the design of a low-power EV that is energy-efficient and cost-effective for urban driving are provided. A highly integrated EM-CVT system, which is efficient, low-cost and lightweight, can be expected for future EV applications.

关键词： electric vehicle co-design continuously variable transmission component sizing optimal control convex programming energy efficiency

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Online Generalized Network Design Under (Dis)Economies of Scale

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MATHEMATICS OF OPERATIONS RESEARCH 2024年第1期49卷 1-651, C2页

作者： Nagarajan, Viswanath Wang, Lily Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA

We consider a general online network design problem in which a sequence of N requests arrive over time, each of which needs to use some subset of the available resources resource. The objective is to minimize the total cost P E. The cost incurred by a resource e E E is some function fe of the total load le on that eEE fe(le). We focus on cost functions that exhibit (dis)economies of scale. These functions are of the form fe(x) = sigma e + xi e center dot x alpha e if x > 0 (and zero if x = 0), in which the exponent alpha e >_ 1. Optimization problems under these functions have received significant recent attention because of applications in energy efficient computing. Our main result is a deterministic online algorithm with tight competitive ratio Theta(maxeEE(sigma e xi e)1=alpha e) when alpha e is constant for all e E E. This framework is applicable to a variety of network design problems in undirected and directed graphs, including multicommodity routing, Steiner tree/forest connectivity, and set connectivity. In fact, our online competitive ratio even matches the previous best (offline) approximation ratio. We also demonstrate the practical performance of our online algorithm on instances of multicommodity routing.

关键词： online algorithms network design convex programming

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Deconvolution of sparse underwater acoustic multipath channel with a large time-delay spread

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JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2010年第2期127卷 909-919页

作者： Zeng, Wen-Jun Jiang, Xue Li, Xi-Lin Zhang, Xian-Da Xiamen Univ Key Lab Underwater Acoust Commun & Marine Informa Minist Educ Xiamen 361005 Peoples R China Sunplus MMobile Inc Beijing Branch Beijing 100085 Peoples R China Univ Maryland Baltimore Cty Dept Comp Sci & Elect Engn Baltimore MD 21250 USA Tsinghua Univ Dept Automat Beijing 100084 Peoples R China

The deconvolution of multipath underwater acoustic channel with a large time-delay spread is investigated. The channel deconvolution involves estimating the multipath time-delays and attenuation factors from a noisy received signal consisting of multiple overlapped signals. Similar to conventional deconvolution methods, the proposed method estimates channel impulse response based on least-squares criterion. However, the proposed method harnesses the sparse structure of an underwater acoustic channel, and l(1)-norm of the channel impulse response is adopted as the cost function to be minimized. In addition, the available a priori knowledge of support constraint and attenuation factor constraint are imposed and channel deconvolution problem is converted to a convex optimization problem. Instead of employing the existing standard algorithms, which require huge storage space and high computational complexity, a simple iterative algorithm for solving the optimization problem with fast convergence rate and low complexity is developed. The computational complexity of the proposed algorithm is O(N log(2)(N)) per iteration with N being the length of the received signal. Simulation results confirm that the proposed method provides better performance in terms of temporal resolution and robustness to noise compared with other extant multipath channel deconvolution techniques.

关键词： acoustic signal processing computational complexity convex programming deconvolution least squares approximations multipath channels transient response underwater acoustic communication

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On LMI-based optimization of vibration and stability in rotor system design

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JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER-TRANSACTIONS OF THE ASME 2006年第3期128卷 677-684页

作者： Cole, Matthew O. T. Wongratanaphisan, Theeraphong Keogh, Patrick S. Chiang Mai Univ Fac Engn Dept Mech Engn Chiang Mai 50200 Thailand Univ Bath Fac Engn & Design Dept Mech Engn Bath BA2 7AY Avon England

This paper considers optimization of rotor system design using stability and vibration response criteria. The initial premise of the study is that the effect of certain design changes can be parametrized in a rotor dynamic model through their influence on the system matrices obtained by finite element modeling. A suitable vibration response measure is derived by considering an unknown,axial distribution of unbalanced components having bounded magnitude. It is shown that the worst-case unbalanced response is given by an absolute row-sum norm of the system frequency response matrix. The minimization of this norm is treated through the formulation of a set of linear matrix inequalities that can also incorporate design parameter constraints and stability criteria. The formulation can also be extended to cover uncertain or time-varying system dynamics arising, for example, due to speed-dependent bearing coefficients or gyroscopic effects. Numerical solution of the matrix inequalities is tackled using an iterative method that involves standard. convex optimization routines. The method is applied in a case study that considers the optimal selection of bearing support stiffness and damping levels to minimize the worst-case vibration of a flexible rotor over a finite speed range. The main restriction in the application of the method is found to be the slow convergence of the numerical routines that occurs with high-order models and/or high problem complexity.

关键词： rotors vibrations stability criteria frequency response finite element analysis convex programming iterative methods machine bearings damping linear matrix inequalities time-varying systems

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An Efficient Hybrid Algorithm for the Separable convex Quadratic Knapsack Problem

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ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 2016年第3期42卷 22-22页

作者： Davis, Timothy A. Hager, William W. Hungerford, James T. Texas A&M Univ Dept Comp Sci & Engn 425E HRBright Bldg3112 TAMU College Stn TX 77843 USA Univ Florida Dept Math 358 Little HallBox 118105 Gainesville FL 32611 USA MAIOR Lucca Italy

This article considers the problem of minimizing a convex, separable quadratic function subject to a knapsack constraint and a box constraint. An algorithm called NAPHEAP has been developed to solve this problem. The algorithm solves the Karush-Kuhn-Tucker system using a starting guess to the optimal Lagrange multiplier and updating the guess monotonically in the direction of the solution. The starting guess is computed using the variable fixing method or is supplied by the user. A key innovation in our algorithm is the implementation of a heap data structure for storing the break points of the dual function and computing the solution of the dual problem. Also, a new version of the variable fixing algorithm is developed that is convergent even when the objective Hessian is not strictly positive definite. The hybrid algorithm NAPHEAP that uses a Newton-type method (variable fixing method, secant method, or Newton's method) to bracket a root, followed by a heap-based monotone break point search, can be faster than a Newton-type method by itself, as demonstrated in the numerical experiments.

关键词： Continuous quadratic knapsack nonlinear programming convex programming quadratic programming separable programming heap

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A Linearized Alternating Direction Method of Multipliers with Substitution Procedure

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2015年第3期32卷 1550011-1550011页

作者： Chao, Miantao Cheng, Caozong Zhang, Haibin Beijing Univ Technol Dept Math Beijing 100124 Peoples R China

We consider the linearly constrained separable convex programming problem whose objective function is separable into m individual convex functions with non-overlapping variables. The alternating direction method of multipliers (ADMM) has been well studied in the literature for the special case m = 2, but the direct extension of ADMM for the general case m >= 2 is not necessarily convergent. In this paper, we propose a new linearized ADMM-based contraction type algorithms for the general case m >= 2. For the proposed algorithm, we prove its convergence via the analytic framework of contractive type methods and we derive a worst-case O(1/t) convergence rate in ergodic sense. Finally, numerical results are reported to demonstrate the effectiveness of the proposed algorithm.

关键词： Alternating direction method of multipliers convex programming convergence rate contraction methods

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