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Simultaneous blind separation of instantaneous mixtures with arbitrary rank

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2006年第10期53卷 2287-2298页

作者： Liu, Derong Hu, Sanqing Zhang, Huaguang Univ Illinois Dept Elect & Comp Engn Chicago IL 60607 USA Mayo Clin & Mayo Fdn Dept Neurol Rochester MN 55905 USA Northeastern Univ Sch Informat Sci & Engn Shenyang 110004 Liaoning Peoples R China

This paper presents a gradient-based method for simultaneous blind separation of arbitrarily linearly mixed source signals. We consider the regular case (i.e., the mixing matrix has full column rank) as well as the ill-conditioned case (i.e., the mixing matrix does not have full column rank). We provide one necessary and sufficient condition for the identifiability of simultaneous blind separation. According to our identifiability condition and the existing general identifiability condition, all source signals are separated into two categories: separable single sources and inseparable mixtures of several single sources. A sufficient condition is also derived for the existence of optimal partition of the mixing matrix which leads to a unique maximum set of separations. One sufficient condition is proved to show that each maximum partition of the mixing matrix corresponds to a unique class of separated signals and as a result we can determine the number of maximum partitions from the classes of outputs under different separation matrices. For sub-Gaussian or super-Gaussian source signals, a cost function based on fourth-order cumulants is introduced to simultaneously separate all separable single sources and all inseparable mixtures. By minimizing the cost function, a gradient-based method is developed. Finally, simulation results show the effectiveness of the present method.

关键词： blind source separation cumulants gradient-based method ill-conditioned case independence maximum partition

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A General Descent Aggregation Framework for gradient-based Bi-Level Optimization

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2023年第1期45卷 38-57页

作者： Liu, Risheng Mu, Pan Yuan, Xiaoming Zeng, Shangzhi Zhang, Jin Dalian Univ Technol DUT RU Int Sch Informat Sci & Engn Dalian 116024 Peoples R China Zhejiang Univ Technol Coll Comp Sci & Technol Hangzhou 310023 Peoples R China Dalian Univ Technol Sch Math Sci Dalian 116024 Peoples R China Univ Hong Kong Dept Math Hong Kang Peoples R China Univ Victoria Dept Math & Stat Victoria BC V8P 5C2 Canada Southern Univ Sci & Technol SUSTech Int Ctr Math Natl Ctr Appl Math Shenzhen Dept Math Shenzhen 518055 Guangdong Peoples R China

In recent years, a variety of gradient-based methods have been developed to solve Bi-Level Optimization (BLO) problems in machine learning and computer vision areas. However, the theoretical correctness and practical effectiveness of these existing approaches always rely on some restrictive conditions (e.g., Lower-Level Singleton, LLS), which could hardly be satisfied in real-world applications. Moreover, previous literature only proves theoretical results based on their specific iteration strategies, thus lack a general recipe to uniformly analyze the convergence behaviors of different gradient-based BLOs. In this work, we formulate BLOs from an optimistic bi-level viewpoint and establish a new gradient-based algorithmic framework, named Bi-level Descent Aggregation (BDA), to partially address the above issues. Specifically, BDA provides a modularized structure to hierarchically aggregate both the upper- and lower-level subproblems to generate our bi-level iterative dynamics. Theoretically, we establish a general convergence analysis template and derive a new proof recipe to investigate the essential theoretical properties of gradient-based BLO methods. Furthermore, this work systematically explores the convergence behavior of BDA in different optimization scenarios, i.e., considering various solution qualities (i.e., global/local/stationary solution) returned from solving approximation subproblems. Extensive experiments justify our theoretical results and demonstrate the superiority of the proposed algorithm for hyper-parameter optimization and meta-learning tasks. Source code is available at https://***/vis-opt-group/BDA.

关键词： Bi-level optimization gradient-based method descent aggregation hyper-parameter optimization meta-learning

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Joint optimization for area traffic control and network flow

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COMPUTERS & OPERATIONS RESEARCH 2005年第11期32卷 2821-2841页

作者： Chiou, SW Natl Dong Hwa Univ Dept Informat Management Hualien 974 Taiwan

A joint optimization problem for solving area traffic control and network flow is investigated. A bilevel programming is used to formulate this joint optimization problem where the network flow following Wardrop's principles can be obtained by solving traffic assignment problems. In this paper, we present a solution approach for jointly optimizing the area traffic control and network flow on the basis of a newly presented algorithm for concurrent flow (Comput. Oper. Res. (2004) in press). We propose three kinds of formulations for this joint optimization problem and present a gradient-based method to effectively solve this problem via a mixture of locally optimal search and global search heuristic where a near global optimum may be found. Numerical comparisons are made for the values of performance index achieved by the joint optimization problem with system optimal flow and those did by equilibrium flow at various sets of initial signal settings. Substantially good results have demonstrated the robustness of the proposed algorithm in solving both system optimal and user equilibrium flow for the joint optimization problem at large-scale networks. (c) 2004 Elsevier Ltd. All rights reserved.

关键词： Wardrop's principles network flow area traffic control gradient-based method

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leShort-term scheduling of thermal power systems using hybrid gradient based modified teaching-learning optimizer with black hole algorithm

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ELECTRIC POWER SYSTEMS RESEARCH 2014年 108卷 16-34页

作者： Azizipanah-Abarghooee, Rasoul Niknam, Taher Bavafa, Farhad Zare, Mohsen Shiraz Univ Technol Dept Elect & Elect Engn Shiraz Iran Islamic Azad Univ Dept Elect Engn Marvdasht Branch Marvdasht Iran

Nowadays, a challengeable subject facing the electric power system operator is how to manage optimally the power generating units over a scheduling horizon of one day considering all of the practical equality, inequality and dynamic constraints. These constraints are comprised of load plus transmission losses balance, valve-point effects, prohibited operating zones, multi-fuel options, line flow constraints, operating reserve and minimum on/off time. In this regard, the proposed framework first presents a practical formulation for the short-term thermal generation scheduling (STGS). It has high-dimensional, high-constraints, non-convex,.non-smooth and non-linear nature and needs an efficient algorithm to be solved. Then, a new optimization approach, known as gradient-based modified teaching-learning-based optimization combined with black hole (MTLBO-BH) algorithm, has been proposed to seek the optimum operational cost. Despite the superior characteristics of the MTLBO and BH algorithms, both of them suffer from the problem of entrapping in local optima. Consequently, the powerful combination of MTLBO and BH and a novel self-adaptive wavelet mutation operator for the organization of the new robust algorithm are proposed in this work. Although the MTLBO-BH algorithm has many properties, some problems still remain to be solved pleasantly. One of these problems is the produced further robust solution that the classical gradient-based technique can overcome it. Finally, performance of the suggested technique is tested on different thermal power systems. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Black hole algorithm gradient-based method Modified teaching-learning-based optimization Prohibited operating zones Short-term thermal generation scheduling Valve-point effect

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Fixed-Time gradient Dynamics With Time-Varying Coefficients for Continuous-Time Optimization

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2023年第7期68卷 4383-4390页

作者： Nguyen, Lien T. T. Yu, Xinghuo Eberhard, Andrew Li, Chaojie RMIT Univ Sch Sci Melbourne Vic 3000 Australia RMIT Univ Sch Engn Melbourne Vic 3000 Australia Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW 2033 Australia

In this article, we propose fixed-time gradient dynamics with time-varying coefficients for continuous-time optimization. We first investigate the Lyapunov stability conditions that allow us to achieve fixed-time stability of the time-varying dynamical systems. We then use them to deal with continuous-time optimization problems. We show that under the proposed fixed-time gradient dynamics and by choosing time-varying coefficients, the searching trajectories converge to their optima in fixed-time from any initial points with a very fast rate. Simulation results are given to show the effectiveness of the proposed fixed-time gradient dynamics with tunable time-varying coefficients for continuous-time optimization.

关键词： Continuous-time optimization fixed-time convergence gradient-based method Lyapunov function Newton-like method stability time-varying systems

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A New Assisted History Matching Approach for Complex Reservoirs

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ENERGY SOURCES PART A-RECOVERY UTILIZATION AND ENVIRONMENTAL EFFECTS 2015年第18期37卷 1954-1961页

作者： Dang, T. Q. C. Chen, Z. Nguyen, T. B. N. Bae, W. Phung, T. H. Univ Calgary Dept Chem & Petr Engn Calgary AB T2N 1N4 Canada Sejong Univ Dept Energy & Mineral Resources Engn Seoul 143747 South Korea Vietsovpetro JV Res & Engn Inst Vung Tau City Vietnam

This article describes the integration of mathematical models (Simplex and steepest descent algorithm) with global modification (through deeply geological studies) to increase the efficiency of history matching. This method can take full advantage of the gradient-based method (fast rate of convergence) and guarantee of finding a global minimum for inverse problems. The above method is applied to the Lower Miocene reservoir at White Tiger field, a highly heterogeneous reservoir, which has been producing under a naturally edge-water mechanism. A model that covers the upper formation of White Tiger field with 27 production wells and 8 injection wells is conditioned to 23 years of production history. The new assisted history matching approach provides an excellent match between simulation results and production data.

关键词： assisted history matching global optimization gradient-based method simplex algorithm steepest descent algorithm

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Time-delayed decentralized H2/LQG controller for cable-stayed bridge under seismic loading

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STRUCTURAL CONTROL & HEALTH MONITORING 2013年第3期20卷 354-372页

作者： Fallah, Arash Yeganeh Taghikhany, Touraj Amirkabir Univ Technol Dept Civil & Environm Engn Tehran Iran

Consistency of real-time data transmission is an important factor in active and semi-active control of structures. Recent advances in wireless sensors and their reliable data communication have attracted many attentions in structural control engineering. Wireless sensors have been also preferred to wire-base types because of problems associated with installing extensive length of coaxial wires. In addition, embedded computing technologies in wireless sensors as local controller reduce size of transferring data and provide stable transmission. However, there are some issues in implementation of wireless connection like communication range and latency. This study presents the feasibility of developing a decentralized controller by using H2/LQG as robust-optimum algorithm in cable-stayed bridge. Because of large scale of structure, the order of model is reduced by using two different reduction methods in finite time and frequency. The controller is developed in centralized and decentralized solutions. The decentralized controller through developing a gradient-based method is designed to efficiently solve system of closed-loop H2 optimization problem. The structural responses in centralized and decentralized solutions are compared with each other under three different earthquake records considering time delay in data transmission. Results indicate that for large-scale bridges with time-delayed data communication issue, H2/LQG controller in decentralized solution gives maximum reduction of response indices in comparison with other strategies. Copyright (C) 2011 John Wiley & Sons, Ltd.

关键词： H2 LQG decentralized time delay model order reduction gradient-based method

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Bilevel programming for the continuous transport network design problem

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TRANSPORTATION RESEARCH PART B-methodOLOGICAL 2005年第4期39卷 361-383页

作者： Chiou, SW Natl Dong Hwa Univ Dept Informat Management Hualien 97401 Taiwan

A Continuous Network Design Problem (CNDP) is to determine the set of link capacity expansions and the corresponding equilibrium flows for which the measures of performance index for the network Is optimal. A bilevel programming technique can be used to formulate this equilibrium network design problem. At the upper level problem, the system performance index is defined as the sum of total travel times and investment costs of link capacity expansions. At the lower level problem. the user equilibrium flow is determined by Wardrop's first principle and can be formulated as an equivalent minimization problem. In this paper we exploit a descent approach via the implementation of gradient-based methods to solve CNDP generally where the Karush-Kuhn-Tucker points can be obtained. Four variants of gradient-based methods are presented and numerical comparisons are widely made with the previous on three kinds of test networks. The proposed methods have achieved substantially better results in terms of the robustness to the initials and the computational efficiency in solving equilibrium assignment problems than did others especially when the congested road networks are considered. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： network design problem bilevel programming gradient-based method

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A comparison of least squares and maximum likelihood methods using sine fitting in ADC testing

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MEASUREMENT 2013年第10期46卷 4362-4368页

作者： Saliga, Jan Kollar, Istvan Michaeli, Linus Busa, Jan Liptak, Jozef Virosztek, Tamas Tech Univ Kosice Kosice 04120 Slovakia Budapest Univ Technol & Econ Budapest Hungary

ADC test methods require the best possible reconstruction of the input signal of the ADC under test from the acquired, therefore erroneous, ADC output data. The commonly used least squares (LS) fit and the recently introduced maximum likelihood (ML) estimation are competing methods. This paper presents a simulation-based comparative study of these estimation methods with the goal to investigate the behavior of both methods and to determine their limits. Two alternative algorithms for the calculation of the maximum likelihood fit are considered (gradient-based minimization and differential evolution). The main finding is that while for low-INL (linear) ADCs the two methods (LS and ML) give similar results, for practical (almost always nonlinear) ADCs ML is definitely better. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： ADC test Maximum likelihood estimation Least squares method LS method Four-parameter fit Signal recovery Estimation of signal parameters gradient-based method Differential evolution

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Finding tradeoffs by using multiobjective optimization algorithms

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TRANSACTIONS OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES 2004年第155期47卷 51-58页

作者： Obayashi, S Sasaki, D Oyama, A Tohoku Univ Inst Fluid Sci Sendai Miyagi Japan Tohoku Univ Dept Syst Informat Sci Sendai Miyagi Japan NASA Glenn Res Ctr Cleveland OH USA

The objective of the present study is to demonstrate performances of Evolutionary Algorithms (EAs) and conventional gradient-based methods for finding Pareto fronts. The multiobjective optimization algorithms are applied to analytical test problems as well as to the real-world problems of a compressor design. The comparison results clearly indicate the superiority of EAs in finding tradeoffs.

关键词： aerodynamics CFD design compressor multiobjective optimization evolutionary computation gradient-based method

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