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International Conference on Industrial Engineering and Systems Management (IESM)

作者： Liu, Ming Yang, Xuenan Tongji Univ Sch Econ & Management Shanghai Peoples R China

ISBN: (纸本)9781728115665

This paper considers an inverse single machine scheduling problem, the forward version of which tries to minimize the maximum lateness (i.e., L-max). In the forward version, with critical parameters such as due dates and processing times are certain and cannot be adjusted. While in this investigated inverse optimization problem, the due dates can be adjusted, and the goal of this problem is to find optimal adjusted due dates, with which the predefined schedule could be an optimal schedule. For this problem, we first analyse the property of the optimal solution when the due dates are certain. Then, with this property, we formulate a convex programming for the investigated problem, and devise a solution method accordingly. To the best of our knowledge, we are the first to provide solvable mathematical programming model for inverse scheduling problems. The validity of the mathematical model and the proposed solution method is demonstrated by a randomly generated instance.

关键词： maximum lateness minimization norm inverse scheduling convex programming

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convex programming model for inverse scheduling with adjustable release times 16

Convex programming model for inverse scheduling with adjusta...

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16th International Conference on Service Systems and Service Management (ICSSSM)

作者： Liu, Ming Yang, Xuenan Tongji Univ Sch Econ & Management Shanghai Peoples R China

ISBN: (纸本)9781728119410

This paper proposes an inverse scheduling problem in a single machine system. The maximum completion time is concerned, the release times are adjustable parameters, and the processing sequence of all jobs is known and fixed. The aim of this inverse scheduling problem is to obtain optimal adjusted release times, which not only have a minimal derivation from the original release times, but also could guarantee the prefixed processing sequence to be optimal. To efficiently solve this problem, we first discuss the properties of optimal solutions of the 1 vertical bar r(i)vertical bar C-max problem. Then, we formulate the investigated inverse scheduling problem into a convex programming model. Based on this model, we further propose a solution method for the investigated inverse scheduling problem. A randomly generated testing instance demonstrates the efficiency of the formulated convex programming model and the proposed method.

关键词： Maximum completion minimization Inverse scheduling Norm convex programming

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convex programming for Nonideal Antenna Array Synthesis Based on Interval Analysis 5

Convex Programming for Nonideal Antenna Array Synthesis Base...

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5th International Conference on Fuzzy Systems and Data Mining (FSDM)

作者： Zhang, Ying Sun, Weirong Kuang, Lin Feng, Jian Shen, Xiaofeng Univ Elect Sci & Technol China Sch Informat & Commun Engn Chengdu Peoples R China

ISBN: (纸本)9781643680194;9781643680187

Array mismatch which is caused by hardware and installation precision affects performance of antenna array significantly. Probability statistics is usually used to model array mismatch, so as to simulate array pattern. In this paper, the non-probabilistic interval analysis (IA) method is used to analyze the bounds of array pattern of uniform linear arrays in view of independent and simultaneous existence of amplitude and phase errors on array excitation. Based on the derived theoretical bounds of array pattern, array synthesis algorithm based on convex optimization is proposed. Compared with the algorithm using global random search, the proposed method can obtain better array excitation parameters with the same array mismatch. Computer simulation results verify the effectiveness and robustness of the proposed algorithm.

关键词： Antenna array array mismatch convex programming interval analysis

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Asymptotic Performance of Sparse Signal Detection Using convex programming Method

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Chinese Journal of Aeronautics 2012年第3期25卷 396-405页

作者： LEI Chuan ZHANG Jun School of Electronics and Information Engineering Beihang UniversityBeijing 100191China National Key Laboratory of CNS/ATM Beijing 100191China

The detection of sparse signals against background noise is considered. Detecting signals of such kind is difficult since only a small portion of the signal carries information. Prior knowledge is usually assumed to ease detection. In this paper, we consider the general unknown and arbitrary sparse signal detection problem when no prior knowledge is available. Under a Ney- man-Pearson hypothesis-testing framework, a new detection scheme is proposed by combining a generalized likelihood ratio test （GLRT）-Iike test statistic and convex programming methods which directly exploit sparsity in an underdetermined system of linear equations. We characterize large sample behavior of the proposed method by analyzing its asymptotic performance. Specifically, we give the condition for the Chernoff-consistent detection which shows that the proposed method is very sensitive to the norm energy of the sparse signals. Both the false alam rate and the miss rate tend to zero at vanishing signal-to-noise ratio （SNR）, as long as the signal energy grows at least logarithmically with the problem dimension. Next we give a large deviation analysis to characterize the error exponent for the Neyman-Pearson detection. We derive the oracle error exponent assuming signal knowledge. Then we explicitly derive the error exponent of the proposed scheme and compare it with the oracle exponent. We complement our study with numerical experiments, showing that the proposed method performs in the vicinity of the likelihood ratio test （LRT） method in the finite sample scenario and the error probability degrades exponentially with the number of observations.

关键词： signal detection convex programming asymptotic analysis signal reconstruction sparse signals

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Joint transmit and receive beamforming for MIMO interference channels using the difference of convex programming

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ANNALS OF TELECOMMUNICATIONS 2021年第11-12期76卷 787-800页

作者： Danesh, Negin Sheikhan, Mansour Mahboobi, Behrad Islamic Azad Univ Dept Elect Engn South Tehran Branch Tehran Iran Islamic Azad Univ Sci & Res Branch Dept Elect & Comp Engn Commun Comp & Ind Network Res Ctr Tehran Iran

Interference alignment (IA) techniques raise the achievable degree of freedom (DoF) in wireless interference networks by designing the aligned transceiver beamformers. The DoF shows the number of interference-free data streams that can be communicated simultaneously on a channel. To achieve the maximum possible DoF, we design the aligned beamformers in this study based on the interference leakage minimization (ILM) method for a multiple-input multiple-output interference channel (MIMO-IC). Accordingly, the ILM optimization problem is firstly relaxed to the rank constrained semidefinite programming (SDP) problems. Next, using a non-convex programming method (i.e., the difference of convex [DC] programming method), the proposed non-convex rank constrained SDP problem is reformulated to the DC form. We propose a novel DC-based IA algorithm that designs the optimized aligned beamformers based on an iterated local search using a penalty function. By increasing the penalty factor, the solution of the penalized DC problem converges to the solution of the original DC problem. Unlike the previous IA approaches, the proposed DC-based IA algorithm optimizes transmit and receive beamformers jointly and simultaneously in each iteration (i.e., not alternately). Simulation results indicate that the proposed method outperforms the previous competitive IA algorithms by providing more throughputs and less interference leakage as compared to the least-squares (LS)-based and the minimum mean square error (MMSE)-based IA algorithms.

关键词： Beamforming MIMO interference channels convex programming

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Blind Deconvolution Using convex programming

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IEEE TRANSACTIONS ON INFORMATION THEORY 2014年第3期60卷 1711-1732页

作者： Ahmed, Ali Recht, Benjamin Romberg, Justin Georgia Tech Sch Elect & Comp Engn Atlanta GA 30332 USA Univ Wisconsin Dept Comp Sci Madison WI 53703 USA

We consider the problem of recovering two unknown vectors, w and x, of length L from their circular convolution. We make the structural assumption that the two vectors are members of known subspaces, one with dimension N and the other with dimension K. Although the observed convolution is nonlinear in both w and x, it is linear in the rank-1 matrix formed by their outer product wx*. This observation allows us to recast the deconvolution problem as low-rank matrix recovery problem from linear measurements, whose natural convex relaxation is a nuclear norm minimization program. We prove the effectiveness of this relaxation by showing that, for "generic" signals, the program can deconvolve w and x exactly when the maximum of N and K is almost on the order of L. That is, we show that if x is drawn from a random subspace of dimension N, and w is a vector in a subspace of dimension K whose basis vectors are spread out in the frequency domain, then nuclear norm minimization recovers wx* without error. We discuss this result in the context of blind channel estimation in communications. If we have a message of length N, which we code using a random L x N coding matrix, and the encoded message travels through an unknown linear time-invariant channel of maximum length K, then the receiver can recover both the channel response and the message when L greater than or similar to N + K, to within constant and log factors.

关键词： Blind deconvolution matrix factorizations low-rank matrix compressed sensing channel estimation rank-1 matrix image deblurring convex programming nuclear norm minimization

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A class of ADMM-based algorithms for three-block separable convex programming

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2018年第3期70卷 791-826页

作者： He, Bingsheng Yuan, Xiaoming Southern Univ Sci & Technol Dept Math Shenzhen 518055 Peoples R China Nanjing Univ Dept Math Nanjing 210093 Jiangsu Peoples R China Univ Hong Kong Dept Math Hong Kong Hong Kong Peoples R China

The alternating direction method of multipliers (ADMM) recently has found many applications in various domains whose models can be represented or reformulated as a separable convex minimization model with linear constraints and an objective function in sum of two functions without coupled variables. For more complicated applications that can only be represented by such a multi-block separable convex minimization model whose objective function is the sum of more than two functions without coupled variables, it was recently shown that the direct extension of ADMM is not necessarily convergent. On the other hand, despite the lack of convergence, the direct extension of ADMM is empirically efficient for many applications. Thus we are interested in such an algorithm that can be implemented as easily as the direct extension of ADMM, while with comparable or even better numerical performance and guaranteed convergence. In this paper, we suggest correcting the output of the direct extension of ADMM slightly by a simple correction step. The correction step is simple in the sense that it is completely free from step-size computing and its step size is bounded away from zero for any iterate. A prototype algorithm in this prediction-correction framework is proposed;and a unified and easily checkable condition to ensure the convergence of this prototype algorithm is given. Theoretically, we show the contraction property, prove the global convergence and establish the worst-case convergence rate measured by the iteration complexity for this prototype algorithm. The analysis is conducted in the variational inequality context. Then, based on this prototype algorithm, we propose a class of specific ADMM-based algorithms that can be used for three-block separable convex minimization models. Their numerical efficiency is verified by an image decomposition problem.

关键词： convex programming Alternating direction method of multipliers Splitting methods Contraction Convergence rate

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ALTERNATING DIRECTION METHOD WITH GAUSSIAN BACK SUBSTITUTION FOR SEPARABLE convex programming

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SIAM JOURNAL ON OPTIMIZATION 2012年第2期22卷 313-340页

作者： He, Bingsheng Tao, Min Yuan, Xiaoming Hong Kong Baptist Univ Dept Math Kowloon Hong Kong Peoples R China Nanjing Univ Dept Math Nanjing 210093 Jiangsu Peoples R China

We consider the linearly constrained separable convex minimization problem whose objective function is separable into m individual convex functions with nonoverlapping variables. A Douglas Rachford alternating direction method of multipliers (ADM) has been well studied in the literature for the special case of m = 2. But the convergence of extending ADM to the general case of m >= 3 is still open. In this paper, we show that the straightforward extension of ADM is valid for the general case of m >= 3 if it is combined with a Gaussian back substitution procedure. The resulting ADM with Gaussian back substitution is a novel approach towards the extension of ADM from m = 2 to m >= 3, and its algorithmic framework is new in the literature. For the ADM with Gaussian back substitution, we prove its convergence via the analytic framework of contractive-type methods, and we show its numerical efficiency by some application problems.

关键词： alternating direction method convex programming Gaussian back substitution separable structure

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A convex programming approach for generating guaranteed passive approximations to tabulated frequency-data

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IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS 2004年第2期23卷 293-301页

作者： Coelho, CP Phillips, J Silveira, LM INESC ID Cadence European Labs P-1000 Lisbon Portugal MIT Dept Elect Engn & Comp Sci Cambridge MA 02139 USA Cadence Berkeley Labs Cadence Design Syst San Jose CA 95134 USA Univ Tecn Lisboa IST Dept Elect & Comp Engn P-1000029 Lisbon Portugal

In this paper, we present a methodology for generating guaranteed passive time-domain models of subsystems described by tabulated frequency-domain data obtained through measurement or through physical simulation. Such descriptions are commonly used to represent on- and off-chip interconnect effects, package parasitics, and passive devices common in high-frequency integrated circuit applications. The approach, which incorporates passivity constraints via convex optimization algorithms, is guaranteed to produce a passive-system model that is optimal in the sense of having minimum error in the frequency band of interest over all models with a prescribed set of system poles. We demonstrate that this algorithm is computationally practical for generating accurate high-order models of data sets representing realistic, complicated multiinput, multioutput systems.

关键词： behavior modeling convex optimization convex programming interconnect modeling rational fitting system identification

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A convex programming-based algorithm for mean payoff stochastic games with perfect information

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OPTIMIZATION LETTERS 2017年第8期11卷 1499-1512页

作者： Boros, Endre Elbassioni, Khaled Gurvich, Vladimir Makino, Kazuhisa Rutgers State Univ MSIS Dept 100 Rockafellar RdLivingston Campus Livingston NJ 08854 USA Rutgers State Univ RUTCOR 100 Rockafellar RdLivingston Campus Livingston NJ 08854 USA Masdar Inst Sci & Technol POB 54224 Abu Dhabi U Arab Emirates Natl Res Univ Higher Sch Econ Moscow Russia Kyoto Univ RIMS Kyoto 6068502 Japan

We consider two-person zero-sum stochastic mean payoff games with perfect information, or BWR-games, given by a digraph G = (V, E), with local rewards r : E -> Z, and three types of positions: black V-B, white V-W, and random V-R forming a partition of V. It is a long-standing open question whether a polynomial time algorithm for BWR-games exists, even when |V-R| = 0. In fact, a pseudo-polynomial algorithm for BWR-games would already imply their polynomial solvability. In this short note, we show that BWR-games can be solved via convex programming in pseudo-polynomial time if the number of random positions is a constant.

关键词： Stochastic games Perfect information Mean payoff Pseudo-polynomial algorithm convex programming

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