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Generalized robust linear discriminant analysis for jointly sparse learning

APPLIED INTELLIGENCE 2024年第19期54卷 9508-9523页

作者： Zhu, Yufei Lai, Zhihui Gao, Can Kong, Heng Shenzhen Univ Coll Comp Sci & Software Engn Shenzhen 518060 Peoples R China Baoan Cent Hosp Shenzhen Dept Breast & Thyroid Surg Shenzhen 518102 Peoples R China

Linear discriminant analysis (LDA) is a well-known supervised method that can perform dimensionality reduction and feature extraction effectively. However, traditional LDA-based methods need to be turned into the trace ratio form to compute the closed-form solution, in which the within-class scatter matrix should be nonsingular. In this article, we design a new model named generalized robust linear discriminant analysis (GRLDA) method to tackle this disadvantage and improve the robustness. GRLDA uses L2,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}_{\mathrm{2,1}}$$\end{document}-norm on both loss functions to reduce the influence of outliers and on regularization term to obtain joint sparsity simultaneously. The intrinsic graph and the penalty graph are constructed to characterize the intraclass similarity and interclass separability, respectively. A novel optimization method is proposed to solve the proposed model, in which a quadratic problem on the Stiefel manifold is involved to avoid the inverse computation on a singular matrix. We also analyze the computational complexity rigorously. Finally, the experimental results on face, object, and medical images exhibit the superiority of GRLDA.

关键词： Generalized Robust Linear Discriminant Analysis (GRLDA) Feature extraction convex optimization problem

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Differential Stability Properties of convex optimization and Optimal Control problems

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JOURNAL OF optimization THEORY AND APPLICATIONS 2024年第2期201卷 609-630页

作者： Toan, Nguyen Thi Thuy, Le Quang Hanoi Univ Sci & Technol Sch Appl Math & Informat 1 Dai Co Viet Hanoi Vietnam

This paper studies the solution stability of convex optimization and discrete convexoptimal control problems in Banach spaces, where the solution set may be *** both the optimization problem and the optimal control problem, formulas forthe epsilon-subdifferential of the optimal value function are derived without qualificationconditions. We first calculate the epsilon-subdifferential of the optimal value function toa parametric optimization problem with geometrical and functional constraints. Wethen use the obtained results to derive a formula for computing the epsilon-subdifferentialof the optimal value function to a discrete convex optimal control problem with linearstate equations, control constraints and initial, terminal conditions

关键词： convex optimization problem convex discrete optimal control problem Optimal value function Conjugate function epsilon-subdifferentials epsilon-normal directions

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Sensor fusion noise suppression method based on finite impulse response complementary filters

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MEASUREMENT 2024年 232卷

作者： Wang, Jing Wang, Lei Lin, Jie Xiao, Ritao Chen, Jiamin Jin, Peng Harbin Inst Technol Sch Instrumentat Sci & Engn 92 Xidazhi St Harbin 150001 Heilongjiang Peoples R China

The noise of an inertial sensor is a major issue that limits low-frequency measurement in active control systems. In order to extend low-frequency measurement bandwidth, an optimal finite impulse response (FIR) complementary filter design method is proposed to fuse a displacement sensor and an inertial sensor in this paper. The equivalent relationship between the system noise and the super-sensor noise is analyzed. The mechanism of complementary filters affecting them is clarified. Then, a value function is first constructed as the optimization objective to minimize the cumulative power spectrum (CPS) of the super sensor noise. Based on this and filter amplitude constraints, a convex optimization problem is constructed for solving the optimal filter coefficients. Finally, the experimental results show that the super sensor based on the proposed filters has a wider lowfrequency bandwidth. The proposed filters are significantly superior to conventional IIR complementary filters.

关键词： Inertial sensor Super sensor Cumulative power spectrum FIR complementary filters convex optimization problem

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An extended projected residual algorithm for solving smooth convex optimization problems

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2022年 412卷

作者： La Cruz, William Univ Cent Venezuela Fac Ingn Dept Elect Comp & Control Caracas 1053 Venezuela

A projected residual algorithm for solving smooth convex optimization problems is presented. The proposed method is an extension of a residual algorithm for solving systems of nonlinear monotone equations introduced by La Cruz (2017), which uses in a systematic way the residual as a search direction combined with the Barzilai-Borwein's choice of the step size and a line search globalization strategy that does not impose the condition that the function value to decrease monotonically at every iteration. The global and R-sublinear convergence of the new method is established. With the aim of showing the advantages of the proposed global scheme an extensive set of numerical experiments including standard test problems and some specific applications are reported. (c) 2022 Elsevier B.V. All rights reserved.

关键词： convex optimization problem Spectral projected gradient method Nonmonotone line search Nonlinear monotone equations

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A fast robust numerical continuation solver to a two-dimensional spectral estimation problem

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IET CONTROL THEORY AND APPLICATIONS 2022年第9期16卷 902-915页

作者： Zhu, Bin Liu, Jiahao Sun Yat Sen Univ Sch Intelligent Syst Engn Waihuan East Rd 132 Guangzhou 510006 Peoples R China

This paper presents a fast algorithm to solve a spectral estimation problem for two-dimensional random fields. The latter is formulated as a convex optimization problem with the Itakura-Saito pseudodistance as the objective function subject to the constraints of moment equations. The structure of the Hessian of the dual objective function is exploited in order to make possible a fast Newton solver. Then the Newton solver is incorporated to a predictor-corrector numerical continuation method which is able to produce a parametrized family of solutions to the moment equations. Two sets of numerical simulations are performed to test the algorithm and spectral estimator. The simulations on the frequency estimation problem show that our spectral estimator outperforms the classical windowed periodograms in the case of two hidden frequencies and has a higher resolution. The other set of simulations on system identification indicates that the numerical continuation method is more robust than Newton's method alone in ill-conditioned instances.

关键词： predictor-corrector methods fast Newton solver convex optimization problem spectral estimator moment equations convex programming 2D spectral estimation problem Newton's method numerical simulations 2D random fields Itakura-Saito pseudodistance Newton method spectral analysis dual objective function fast robust numerical continuation solver numerical analysis frequency estimation predictor-corrector numerical continuation method frequency estimation problem objective function subject

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On the Douglas-Rachford Algorithm for Solving Possibly Inconsistent optimization problems

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

作者： Bauschke, Heinz H. Moursi, Walaa M. Univ British Columbia Math Kelowna BC V1V 1V7 Canada Univ Waterloo Dept Combinator & Optimizat Waterloo ON N2L 3G1 Canada Mansoura Univ Fac Sci Math Dept Mansoura 35516 Egypt

More than 40 years ago, Lions and Mercier introduced in a seminal paper the Douglas-Rachford algorithm. Today, this method is well-recognized as a classic and highly successful splitting method to find minimizers of the sum of two (not necessarily smooth) convex functions. Whereas the underlying theory has matured, one case remains a mystery: the behavior of the shadow sequence when the given functions have disjoint domains. Building on previous work, we establish for the first time weak and value convergence of the shadow sequence generated by the Douglas-Rachford algorithm in a setting of unprecedented generality. The weak limit point is shown to solve the associated normal problem, which is a minimal perturbation of the original optimization problem. We also present new results on the geometry of the minimal displacement vector.

关键词： convex functions convex optimization problem Douglas-Rachford algorithm inconsistent optimization problem minimal displacement vector normal problem proximal mapping resolvent

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A New Gradient Projection Algorithm for convex Minimization problem and its Application to Split Feasibility problem

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VIETNAM JOURNAL OF MATHEMATICS 2022年第1期50卷 29-44页

作者： Erturk, Muzeyyen Kizmaz, Asiye Adiyaman Univ Dept Math Adiyaman Turkey

In this paper, we study convergence analysis of a new gradient projection algorithm for solving convex minimization problems in Hilbert spaces. We observe that the proposed gradient projection algorithm weakly converges to a minimum of convex function f which is defined from a closed and convex subset of a Hilbert space to Double-struck capital R. Also, we give a nontrivial example to illustrate our result in an infinite dimensional Hilbert space. We apply our result to solve the split feasibility problem.

关键词： Gradient projection algorithm convex optimization problem Fixed point Split feasibility problem

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An Approximate Penalty Method with Descent for convex optimization problems

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RUSSIAN MATHEMATICS 2019年第7期63卷 41-55页

作者： Konnov, I. V. Kazan Fed Univ Dept Syst Anal & Informat Technol 18 Kremlyovskaya Str Kazan 420008 Russia

We propose a penalty method for general convex constrained optimization problems, where each auxiliary penalized problem is solved approximately with a special composite descent method. Direction finding choice in this method is found with the help of an equivalent equilibrium type problem. This allows one to keep the complete structure of the initial problem, although without nonlinear constraints and to simply calculate the descent direction in separable problems. Convergence of the method in primal and dual variables is established under rather weak assumptions.

关键词： convex optimization problem non-linear constraints penalty method descent method decomposition

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A Novel Decomposition Solution Approach for the Restoration problem in Distribution Networks

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IEEE TRANSACTIONS ON POWER SYSTEMS 2020年第5期35卷 3810-3824页

作者： Sekhavatmanesh, Hossein Cherkaoui, Rachid Ecole Polytech Fed Lausanne EPFL Power Syst Res Grp CH-1015 Lausanne Switzerland

The distribution network restoration problem is by nature a mixed integer and non-linear optimization problem due to the switching decisions and Optimal Power Flow (OPF) constraints, respectively. The link between these two parts involves logical implications modelled through big-M coefficients. The presence of these coefficients makes the relaxation of the mixed-integer problem using branch-and-bound method very poor in terms of computation burden. Moreover, this link inhibits the use of classical Benders algorithm in decomposing the problem because the resulting cuts will still depend on the big-M coefficients. In this paper, a novel decomposition approach is proposed for the restoration problem named Modified Combinatorial Benders (MCB). In this regard, the reconfiguration problem and the OPF problem are decomposed into master and sub problems, which are solved through successive iterations. In the case of a large outage area, the numerical results show that the MCB provides, within a short time (after a few iterations), a restoration solution with a quality that is close to the proven optimality when it can be exhibited.

关键词： optimization Circuit faults Load flow Switches Network topology Computational modeling convex optimization problem decomposition distribution network load pickup line switches reconfiguration restoration service

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Periodical sparse low-rank matrix estimation algorithm for fault detection of rolling bearings

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ISA TRANSACTIONS 2020年 101卷 366-378页

作者： Wang, Baoxiang Liao, Yuhe Ding, Chuancang Zhang, Xining Xi An Jiao Tong Univ Sch Mech Engn Shaanxi Key Lab Mech Prod Qual Assurance & Diagno Xian 710049 Shaanxi Peoples R China Xi An Jiao Tong Univ Educ Minist Modern Design & Rotor Bearing Syst Key Lab Xian 710049 Peoples R China Xi An Jiao Tong Univ Sch Mech Engn State Key Lab Mfg Syst Engn Xian 710049 Shaanxi Peoples R China

Early bearing fault detection is crucial to avoid catastrophic accidents. However, the repetitive defect impulses indicating bearing fault are buried in heavy background noise. In the paper, a novel periodical sparse low-rank (PSLR) matrix estimation algorithm is proposed for extracting repetitive transients from noisy signal. Concretely, periodical group sparsity and low-lank property of fault transients in time-frequency domain are first revealed, and then an optimization problem is proposed for simultaneously promoting these two properties. Meanwhile, to further highlight the sparsity of fault features, the non-convex penalty functions are incorporated into the optimization problem. Then, for solving the proposed optimization problem, an iterative algorithm is derived based on alternating direction method of multipliers (ADMM) and majorization-minimization (MM), in which the traditional soft-thresholding operation is replaced by the proposed Gini-guided fault information thresholding (FIT) scheme to enhance fault transient extraction. Finally, simulated and real signals confirm the performance of proposed PSLR in extracting defect impulses from noisy vibration signal. (c) 2020 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： Periodical sparse low-rank (PSLR) matrix estimation convex optimization problem Gini-guided fault information thresholding (FIT) scheme Fault detection Rolling bearings

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