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nonconvex function activated zeroing neural network models for dynamic quadratic programming subject to equality and inequality constraints

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NEUROCOMPUTING 2017年 267卷 107-113页

作者： Jin, Long Li, Shuai Lanzhou Univ Sch Informat Sci & Engn Lanzhou Gansu Peoples R China Hong Kong Polytech Univ Dept Comp Kowloon Hong Kong Peoples R China

Zeroing neural network (ZNN, or termed Zhang neural network after its inventor), being a special type of neurodynamic methodology, has shown powerful abilities to solve a great variety of time-varying problems with monotonically increasing odd activation functions. However, the existing results on ZNN cannot handle the inequality constraint in the optimization problem and nonconvex function cannot applied to accelerating the convergence speed of ZNN. This work breaks these limitations by proposing ZNN models, allowing nonconvex sets for projection operations in activation functions and incorporating new techniques for handing inequality constraint arising in optimizations. Theoretical analyses reveal that the proposed ZNN models are of global stability with timely convergence. Finally, illustrative simulation examples are provided and analyzed to substantiate the efficacy and superiority of the proposed ZNN models for real-time dynamic quadratic programming subject to equality and inequality constraints. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Zeroing neural network Quadratic programming nonconvex function Inequality constraint

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nonconvex low-rank regularization method for video snapshot compressive imaging

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APPLIED MATHEMATICAL MODELLING 2025年第PartA期137卷

作者： Li, Min Hu, Huanran Yang, Ming Han, Yu Shenzhen Univ Sch Math Sci Shenzhen Key Lab Adv Machine Learning & Applicat Shenzhen 518060 Peoples R China Harbin Engn Univ Coll Math Sci Harbin 150001 Heilongjiang Peoples R China

The reconstruction of snapshot compressive imaging (SCI) presents a significant challenge in signal processing. The primary goal of SCI is to employ a low-dimensional sensor to capture high-dimensional data in a compressed form. As a result, compared to traditional compressive sensing, SCI emphasizes capturing structural information and enhancing the reconstruction quality of high-dimensional videos and hyperspectral images. This paper proposes a novel SCI reconstruction method by integrating non-convex regularization approximation in conjunction with rank minimization. Furthermore, we address the characterization of structural information by leveraging nonlocal self-similarity across video frames to improve the reconstruction quality. We also develop an optimization algorithm based on the alternating direction method of multipliers (ADMM) to solve the model and provide a convergence algorithm analysis. Extensive experiments demonstrate that the proposed approach can potentially reconstruct SCI effectively.

关键词： Snapshot compressive imaging Video processing nonconvex function Low-rank regularization

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Minimization of a class of nonconvex functions

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Cybernetics 1974年第4期10卷 627-632页

作者： Kantsedal, S.A. Maksimov, Yu.B.

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On the solution of two-stage stochastic problems with nonconvex functions

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Cybernetics 1976年第3期12卷 437-439页

作者： Ermolenko, O.V.

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Sparse Aperture ISAR Imaging Method Based on Joint Constraints of Sparsity and Low Rank

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2021年第1期59卷 168-181页

作者： Zeng, Chuangzhan Zhu, Weigang Jia, Xin Yang, Liu Space Engn Univ Beijing 101416 Peoples R China

A new inverse synthetic aperture radar (ISAR) imaging framework is proposed to obtain high cross-range resolution under sparse aperture conditions, which is a challenge when the signal-to-noise ratio is low. Motivated by the sparsity and low rank of targets 2-D distribution, the imaging problem is converted to the simultaneously sparse and low-rank signal matrix reconstruction problem under multiple measurement vector (MMV) model, and a novel reconstruction method based on joint constraints of sparsity and low rank is proposed. Due to the over-relax problem, the traditional convex optimization method cannot achieve a better performance using joint structures than exploiting just one of the constraints. As such, a nonconvex penalty function is introduced. To avoid the local minima, the convexity of the cost function should be ensured when constructing the nonconvex penalty function. The adaptive filtering framework, which is a powerful way to recovery the sparse low-rank matrix accurately from its noisy observation, is adopted as a reconstruction algorithm. Furthermore, the optimal step size formula and the idea of smoothed zero norm are used to enhance the convergence and the ability to suppress noise. The newly proposed method is verified by the simulation experiment, which has a better performance in image quality, robustness to noise, and imaging speed.

关键词： Image reconstruction Apertures Reconstruction algorithms Sparse matrices Radar imaging Signal to noise ratio Adaptive filters compressed sensing inverse synthetic aperture radar (ISAR) low rank nonconvex function sparse aperture

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A new Liu-Storey type nonlinear conjugate gradient method for unconstrained optimization problems

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2009年第1期225卷 146-157页

作者： Zhang, Li Changsha Univ Sci & Technol Coll Math & Computat Sci Changsha 410076 Hunan Peoples R China

Although the Liu-Storey (LS) nonlinear conjugate gradient method has a similar structure as the well-known Polak-Ribiere-Polyak (PRP) and Hestenes-Stiefel (HS) methods, research about this method is very rare. In this paper, based on the memoryless BFGS quasi-Newton method, we propose a new LS type method, which converges globally for general functions with the Grippo-Lucidi line search. Moreover, we modify this new LS method such that the modified scheme is globally convergent for nonconvex minimization if the strong Wolfe line search is used. Numerical results are also reported. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Conjugate gradient method nonconvex function Global convergence

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Combinatorial optimisation for pulse position modulation-ultra wideband signal detection based on compressed sensing and analogue-to-information converter

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IET SIGNAL PROCESSING 2016年第5期10卷 543-548页

作者： Wang, Weidong Wang, Shafei Yang, Jun-an Liu, Hui Inst Elect Engn Hefei Peoples R China Key Lab Elect Restrict Hefei Anhui Peoples R China Northen Inst Elect Equipment China Beijing Peoples R China

Pulse position modulation-ultra wideband (PPM-UWB) communication signal is hard to detect and sample directly, owing to its ultra-low power spectral density and wide bandwidth. There are already some researches on using analogue-to-information converter (AIC) technology and compressed sensing (CS) theory to under-sample and detect PPM-UWB communication signal, utilising its sparseness in time domain. However, greedy algorithm lacks of restriction on sparseness of reconstructed vector, while common restrictions on sparseness (e.g. convex optimisation) has high computational complexity. To solve these problems, a combinatorial optimisation method is proposed in this study to detect PPM-UWB communication signal based on CS and AIC. Reconstruction error and sparseness of reconstructed vector are restricted by l(2)- and l(p)-norms, respectively. l(p)-norm (0 < p < 1), which is a non-convex function, has stricter restriction on sparseness than l(1)-norm. Meanwhile, the steepest descent method is adopted for l(p)-norm optimisation, which can rapidly converge to objective values. Proposed method has more comprehensive restriction than greedy algorithm and convex optimisation, while maintain low complexity in computation as greedy algorithm. Numerical experiments demonstrate the validity of proposed method.

关键词： combinatorial mathematics signal detection analogue-digital conversion compressed sensing ultra wideband communication convex programming computational complexity greedy algorithms pulse position modulation-ultra wideband signal detection compressed sensing theory analogue-to-information converter PPM-UWB communication signal ultra-low power spectral density AIC technology greedy algorithm reconstructed vector convex optimisation computational complexity combinatorial optimisation method reconstruction error nonconvex function steepest descent method l(p)-norm optimisation

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Stochastic Bigger Subspace Algorithms for nonconvex Stochastic Optimization

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IEEE ACCESS 2021年 9卷 119818-119829页

作者： Yuan, Gonglin Zhou, Yingjie Wang, Liping Yang, Qingyuan Guangxi Univ Coll Math & Informat Sci Ctr Appl Math Guangxi Nanning 530004 Guangxi Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Sci Nanjing 210016 Jiangsu Peoples R China Nanning Coll Vocat Technol Nanning 530004 Guangxi Peoples R China

It is well known that the stochastic optimization problem can be regarded as one of the most hard problems since, in most of the cases, the values off f and its gradient are often not easily to be solved, or the F(., xi) is normally not given clearly and (or) the distribution function P is equivocal. Then an effective optimization algorithm is successfully designed and used to solve this problem that is an interesting work. This paper designs stochastic bigger subspace algorithms for solving nonconvex stochastic optimization problems. A general framework for such algorithm is presented for convergence analysis, where the so-called the sufficient descent property, the trust region feature, and the global convergence of the stationary points are proved under the suitable conditions. In the worst-case, we will turn out that the complexity is competitive under a given accuracy parameter. We will proved that the SFO-calls complexity of the presented algorithm with diminishing steplength is O(epsilon( -1/1-beta)) and the SFO-calls complexity of the given algorithm with random constant steplength is O(epsilon(-2)) respectively, where beta is an element of (0.5, 1) and epsilon is accuracy and the needed conditions are weaker than the quasi-Newton methods and the normal conjugate gradient algorithms. The detail algorithm framework with variance reduction is also proposed for experiments and the nonconvex binary classification problem is done to demonstrate the performance of the given algorithm.

关键词： Stochastic subspace algorithm nonconvex function convergence property machine learning complexity analysis

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nonconvex Total Generalized Variation Model for Image Inpainting

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INFORMATICA 2021年第2期32卷 357-370页

作者： Liu, Xinwu Hunan Univ Sci & Technol Sch Math & Computat Sci Xiangtan 411201 Hunan Peoples R China

It is a challenging task to prevent the staircase effect and simultaneously preserve sharp edges in image inpainting. For this purpose, we present a novel nonconvex extension model that closely incorporates the advantages of total generalized variation and edge-enhancing nonconvex penalties. This improvement contributes to achieve the more natural restoration that exhibits smooth transitions without penalizing fine details. To efficiently seek the optimal solution of the resulting variational model, we develop a fast primal-dual method by combining the iteratively reweighted algorithm. Several experimental results, with respect to visual effects and restoration accuracy, show the excellent image inpainting performance of our proposed strategy over the existing powerful competitors.

关键词： image inpainting nonconvex function total generalized variation primal-dual method

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Evolution hemivariational inequalities in infinite dimension and their control

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2001年第1期47卷 101-112页

作者： Migorski, S Jagiellonian Univ Fac Math & Phys Inst Comp Sci PL-30072 Krakow Poland

In this note we consider the problem of optimal control for a class of systems governed by evolution hemivariational inequality. First we prove the existence of solutions to the hemivariational. inequality and next we present a result on the existence of optimal controls. Finally we sketch the proof of the existence result for evolution hemivariational inequality of second order.

关键词： hemivariational nonconvex function evolution triple compact embedding multifunction parabolic hyperbolic pseudomonotone operator selection semicontinuity sub differential control problem

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