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INHIBITORY GRIDS AND THE ASSIGNMENT PROBLEM

IEEE TRANSACTIONS ON NEURAL NETWORKS 1993年第2期4卷 319-331页

作者： WOLFE, WJ MACMILLAN, JM BRADY, G MATHEWS, R ROTHMAN, JA MATHIS, D OROSZ, MD ANDERSON, C ALAGHBAND, G Department of Computer Science and Engineering University of Colorado Denver CO USA Dept. of Comput. Sci. & Eng. Colorado Univ. Denver CO USA

This paper analyzes a family of symmetric neural networks that solve a simple version of the Assignment Problem (AP). We analyze the suboptimal performance of these networks and compare the results to optimal answers obtained by linear programming techniques. We use the Interactive Activation model to define the network dynamics-a model that is closely related to the Hopfield-Tank model. A systematic analysis of hypercube corner stability and eigenspaces of the connection strength matrix leads to network parameters that provide feasible solutions 100% of the time and to a novel projection algorithm that significantly improves performance. Two formulations of the problem are discussed: i) nearest corner: encode the assignment numbers as initial activations, and ii) lowest energy corner: encode the assignment numbers as external inputs.

关键词： Neural networks Linear programming Performance analysis Algorithm design and analysis Hypercubes Stability analysis projection algorithms Random number generation Computer science Analog circuits

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Minimum distance between the faces of two convex polyhedra: A sufficient condition

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JOURNAL OF GLOBAL OPTIMIZATION 2003年第4期26卷 361-385页

作者： Llanas, B De Sevilla, MF Feliu, V ETSI Caminos Dpto Matemat & Informat Madrid 28040 Spain ETSI Ind Dpto Ingn Elect Ciudad Real 13071 Spain

The problem of finding the Euclidean distance between two convex polyhedra can be reduced to the combinatorial optimization problem of finding the minimum distance between their faces. This paper presents a global optimality criterion for this problem. An algorithm (QLDPA) for the fast computation of the distance between convex and bounded polyhedra is proposed as an application of it. Computer experiments show its fast performance, especially when the total number of vertices is large.

关键词： distance between convex polyhedra local descent projection algorithms sufficient condition of global minimum

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ON COMPUTING 3-FINGER FORCE-CLOSURE GRASPS OF POLYGONAL OBJECTS

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IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION 1995年第6期11卷 868-881页

作者： PONCE, J FAVERJON, B UNIV ILLINOIS BECKMAN INST URBANA IL 61801 USA ALEPH TECHNOL F-38400 ST MARTIN DHERES FRANCE

This paper addresses the problem of computing stable grasps of 2-D polygonal objects. We consider the case of a hand equipped with three hard fingers and assume point contact with friction. We prove new sufficient conditions for equilibrium and force closure that are linear in the unknown grasp parameters. This reduces computing the stable grasp regions in configuration space to constructing the three-dimensional projection of a five-dimensional polytope. We present an efficient projection algorithm based on linear programming and variable elimination among linear constraints. Maximal object segments where fingers can be positioned independently while ensuring force closure are found by linear optimization within the grasp regions. The approach has been implemented and several examples are presented.

关键词： Fingers Friction Sufficient conditions Space technology Computer science USA Councils projection algorithms Mechanical factors Robots Resists

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A MILDLY WEAKER SUFFICIENT CONDITION IN IIR ADAPTIVE FILTERING

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 1994年第1期42卷 203-206页

作者： NAYERI, M Department of Electrical Engineering Michigan State University East Lansing MI USA

The cross-covariance matrix of two stable autoregressive (AR) sequences is considered. A mildly weaker condition is identified that ensures the nonsingularity of this matrix. As one consequence of this result, a weaker sufficient condition is obtained that would guarantee the unimodality of the mean-square output error surface of an IIR adaptive filter with white noise excitation.

关键词： Sufficient conditions Adaptive filters Image reconstruction Equations IIR filters projection algorithms Signal processing White noise Quantization Upper bound

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Bi-Orthonormal Polynomial Basis Function Framework With Applications in System Identification

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2016年第11期61卷 3285-3300页

作者： van Herpen, Robbert Bosgra, Okko Oomen, Tom Eindhoven Univ Technol Dept Mech Engn Control Syst Technol Grp NL-5612 AZ Eindhoven Netherlands

Numerical aspects are of central importance in identification and control. Many computations in these fields involve approximations using polynomial or rational functions that are obtained using orthogonal or oblique projections. The aim of this paper is to develop a new and general theoretical framework to solve a large class of relevant problems. The proposed method is built on the introduction of bi-orthonormal polynomials with respect to a data-dependent bi-linear form. This bi-linear form generalises the conventional inner product and allows for asymmetric and indefinite problems. The proposed approach is shown to lead to optimal numerical conditioning (kappa = 1) in a recent frequency-domain instrumental variable system identification algorithm. In comparison, it is shown that these recent algorithms exhibit extremely poor numerical properties when solved using traditional approaches.

关键词： Least-squares approximations numerical analysis polynomials projection algorithms system identification

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Decoding Nonbinary LDPC Codes via Proximal-ADMM Approach

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IEEE TRANSACTIONS ON INFORMATION THEORY 2022年第9期68卷 5730-5746页

作者： Wang, Yongchao Bai, Jing Xidian Univ State Key Lab Integrated Serv Networks Xian 710071 Peoples R China Shijiazhuang Tiedao Univ Sch Informat Sci & Technol Shijiazhuang 050043 Hebei Peoples R China

In this paper, we focus on decoding nonbinary low-density parity-check (LDPC) codes in Galois fields of characteristic two via the proximal alternating direction method of multipliers (proximal-ADMM). By exploiting Flanagan/Constant-Weighting embedding techniques and the decomposition technique based on three-variables parity-check equations, two efficient proximal-ADMM decoders for nonbinary LDPC codes are proposed. We show that both of them are theoretically guaranteed convergent to some stationary point of the decoding model and either of their computational complexities in each proximal-ADMM iteration scales linearly with LDPC code's length and the size of the considered Galois field. Moreover, the decoder based on the Constant-Weight embedding technique satisfies the favorable property of codeword symmetry. Simulation results demonstrate their effectiveness in comparison with state-of-the-art LDPC decoders.

关键词： Maximum likelihood decoding Mathematical models Iterative decoding Linear matrix inequalities projection algorithms Heuristic algorithms Convergence Nonbinary low-density parity-check (LDPC) codes Galois fields of characteristic two proximal alternating direction method of multipliers (proximal-ADMM) quadratic programming (QP)

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Non-Linear Reconstruction of Delta-Sigma Modulated Signals: Randomized Surrogate Constraint Decoding Algorithm

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2013年第21期61卷 5361-5373页

作者： Marijan, Malisa Ignjatovic, Zeljko Univ Rochester Rochester NY 14627 USA

Delta-sigma (Delta Sigma) A/D conversion is a popular technique used to achieve high resolution data conversion for low to moderate bandwidth applications. It is commonly accepted that the digital circuitry of the Delta Sigma A/D converters should perform a linear time-invariant (LTI) filtering on the output of the Delta Sigma modulator in order to reconstruct the input signal. However, it has been shown that, when higher order Delta Sigma A/D converters are operated at higher oversampling ratios (OSRs), non-linear reconstruction algorithms extract more information about the input signal than LTI methods. Still, use of non-linear algorithms has been limited due to their complexity and stability issues. Two practical nonlinear methods presented in the literature are fast projection onto convex sets (POCS) and direct projection (DP). In this work, we show that the non-linear reconstruction process for Delta Sigma modulated sequences can be treated as a linear feasibility problem(LFP). We then show that if the reconstruction process is defined as an LFP, its implementation is less complex than in the case of the DP method. We further describe how the LFP can be well-conditioned and demonstrate the reconstruction process by using the surrogate constraint algorithm with random constraint selection. The described algorithm considers a small number of constraints at a time, which makes it suitable for serial implementation.

关键词： Delta-sigma modulation projection algorithms signal reconstruction

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Norm-constrained adaptive algorithms for sparse system identification based on projections onto intersections of hyperplanes

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SIGNAL PROCESSING 2016年 118卷 259-271页

作者： Beck, Eduardo Ortiz Batista, Eduardo Luiz Seara, Rui Univ Fed Santa Catarina Dept Elect & Elect Engn LINSE Circuits & Signal Proc Lab BR-88040900 Florianopolis SC Brazil

This paper introduces a novel approach to derive norm-constrained adaptive algorithms for sparse system identification. In contrast to other similar approaches found in the literature, the proposed approach is focused primarily on keeping the a posteriori error equal to zero (which is a characteristic of the normalized least-mean-square algorithm) while seeking to satisfy a norm constraint. To this end, the proposed algorithms look directly for a vector belonging to the intersection of a zero-error hyperplane and a hyperplane resulting from a relaxed norm constraint. This somewhat simpler strategy leads to effective sparsity-promoting adaptive algorithms that exhibit low computational complexity and use parameters that are easy to adjust. In this context, a general framework that allows obtaining adaptive algorithms using different norm functions is devised. From this framework, two norm-constrained algorithms based on the l(1) and l(0) norms are obtained. Moreover, enhanced versions of these algorithms are developed aiming to make them independent of user-defined norm-bound parameters. Numerical simulation results corroborate the effectiveness of the proposed framework as well as the very good performance of the obtained algorithms. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Adaptive filtering Norm-constrained optimization projection algorithms Sparse impulse response System identification

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Subgradient of Cycle-Based Aging Cost Function and Its Application in Optimal Operation of Battery Energy Storage System With Multiple Subsystems

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IEEE TRANSACTIONS ON ENERGY CONVERSION 2024年第1期39卷 625-643页

作者： Diao, Rui Hu, Zechun Song, Yonghua Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China Univ Macau State Key Lab Internet Things Smart City Macau 999078 Peoples R China

Recently,many researchers have adopted the cycle-based degradation model to estimate the aging of battery energy storage system (BESS) based on the cycle information obtained from the rainflow counting method. However, the lack of a mathematical expression for the rainflow counting method is one of the biggest obstacles to the widespread use of the cycle-based degradation model. This article deduces the exact analytical subgradients of the cycle-based aging cost function, which makes it possible to efficiently solve the optimal operation problem without the mathematical expression of the rainflow counting method. We introduce the subgradient projection algorithm to get the theoretical optimal operation in some special cases where the charge-discharge complementarity constraints can be relaxed. We also develop a heuristic algorithm based on the subgradient method to avoid simultaneous charging and discharging in general cases. The effectiveness of the proposed methodologies has been demonstrated with extensive numerical experiments. In the scenarios discussed in this article, implementing the cycle-based operation rather than the energy-based operation reduces the aging cost by about 12%. When the duration of the simulation is 60 minutes, the computation time of a general-purpose solver is about 74 minutes, and the proposed algorithm only needs 21 seconds.

关键词： Aging Batteries Degradation Cost function State of charge Costs projection algorithms Battery energy storage system optimal operation degradation model rainflow counting method aging cost subgradient

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SUPERLINEAR CONVERGENCE THEOREM IN THE ABSG CLASS OF algorithms FOR NONLINEAR ALGEBRAIC EQUATIONS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1988年第1期59卷 39-43页

作者： ABAFFY, J Institute of Mathematics and Computer Science Karl Marx University of Economics Budapest Hungary

In this paper, it is shown that, when two subclasses of algorithms in the ABSg family are applied to a set of nonlinear algebraic equations, then the convergence is superlinear. The conditions for the theorem to be tr... 详细信息

关键词： conjugate direction methods Nonlinear algebraic equations optimization projection algorithms

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