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A Nonlinearly Preconditioned forward-backward Splitting Method and Applications

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2022年第16期42卷 1880-1895页

作者： Vu, Bang Cong Papadimitriou, Dimitri Huawei Belgium Res Ctr BeRC 3NLab Leuven Belgium

In this paper, we prove the weak convergence of the iterates generated by the nonlinearly preconditioned forward-backward splitting method for the sum of a maximally hypermonotone operator A and a hypercocoercive operator B under several suitable conditions. We provide several choices of the nonlinear preconditioners for solving nonlinearly composed inclusions. In particular, the backward-forward splitting method is recovered by the nonlinearly preconditioned forward-backward splitting method with a special choice of the nonlinear preconditioner.

关键词： Cocoercive composite operator forward-backward algorithm hypercocoercive hypermonotone monotone inclusion monotone operator operator splitting preconditioning

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Finite mixture of hidden Markov models for tensor-variate time series data

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2024年第3期18卷 545-562页

作者： Asilkalkan, Abdullah Zhu, Xuwen Sarkar, Shuchismita Univ Alabama Dept Informat Syst Stat & Management Sci Tuscaloosa AL 35487 USA Bowling Green State Univ Dept Appl Stat & Operat Res Bowling Green OH 43403 USA

The need to model data with higher dimensions, such as a tensor-variate framework where each observation is considered a three-dimensional object, increases due to rapid improvements in computational power and data storage capabilities. In this study, a finite mixture of hidden Markov model for tensor-variate time series data is developed. Simulation studies demonstrate high classification accuracy for both cluster and regime IDs. To further validate the usefulness of the proposed model, it is applied to real-life data with promising results.

关键词： Finite mixture model Hidden Markov model forward-backward algorithm Tensor-variate time series

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DOUBLE INERTIAL PROXIMAL GRADIENT algorithmS FOR CONVEX OPTIMIZATION PROBLEMS AND APPLICATIONS

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Acta Mathematica Scientia 2023年第3期43卷 1462-1476页

作者： Kunrada KANKAM Prasit CHOLAMJIAK School of Science University of PhayaoPhayao56000Thailand

In this paper, we propose double inertial forward-backward algorithms for solving unconstrained minimization problems and projected double inertial forward-backward algorithms for solving constrained minimization problems. We then prove convergence theorems under mild conditions. Finally, we provide numerical experiments on image restoration problem and image inpainting problem. The numerical results show that the proposed algorithms have more efficient than known algorithms introduced in the literature.

关键词： weak convergence forward-backward algorithm convex minimization inertial technique

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On the forward-backward method with nonmonotone linesearch for infinite-dimensional nonsmooth nonconvex problems

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2025年 1-46页

作者： Azmi, Behzad Bernreuther, Marco Univ Konstanz Dept Math & Stat Univ Str 10 D-78457 Constance Germany Univ Stuttgart Inst Ind Mfg & Management IFF Allmandring 35 D-70569 Stuttgart Germany

This paper provides a comprehensive study of the nonmonotone forward-backward splitting (FBS) method for solving a class of nonsmooth composite problems in Hilbert spaces. The objective function is the sum of a Fr & eacute;chet differentiable (not necessarily convex) function and a proper lower semicontinuous convex (not necessarily smooth) function. These problems appear, for example, frequently in the context of optimal control of nonlinear partial differential equations (PDEs) with nonsmooth sparsity-promoting cost functionals. We discuss the convergence and complexity of FBS equipped with the nonmonotone linesearch under different conditions. In particular, R-linear convergence will be derived under quadratic growth-type conditions. We also investigate the applicability of the algorithm to problems governed by PDEs. Numerical experiments are also given that justify our theoretical findings.

关键词： Nonsmooth nonconvex optimization forward-backward algorithm Infinite-dimensional problems Nonmonotone linesearch Quadratic growth PDE-constrained optimization

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Conical averagedness and convergence analysis of fixed point algorithms

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JOURNAL OF GLOBAL OPTIMIZATION 2022年第2期82卷 351-373页

作者： Bartz, Sedi Dao, Minh N. Phan, Hung M. Univ Massachusetts Dept Math Sci Kennedy Coll Sci Lowell MA 01854 USA Federat Univ Australia Sch Engn Informat Technol & Phys Sci Ballarat Vic 3353 Australia

We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the stability under relaxations, convex combinations and compositions. We derive conical averagedness properties of resolvents of generalized monotone operators. These properties are then utilized in order to analyze the convergence of the proximal point algorithm, the forward-backward algorithm, and the adaptive Douglas-Rachford algorithm. Our study unifies, improves and casts new light on recent studies of these topics.

关键词： Adaptive Douglas-Rachford algorithm Cocoercivity Conically averaged operator forward-backward algorithm Proximal point algorithm Strong monotonicity Weak monotonicity

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A Reflected forward-backward Splitting Method for Monotone Inclusions Involving Lipschitzian Operators

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SET-VALUED AND VARIATIONAL ANALYSIS 2021年第1期29卷 163-174页

作者： Cevher, Volkan Bang Cong Vu Ecole Polytech Fed Lausanne Lab Informat & Inference Syst Lausanne Switzerland

In this paper, we propose a novel splitting method for finding a zero point of the sum of two monotone operators where one of them is Lipschizian. The weak convergence the method is proved in real Hilbert spaces. Applying the proposed method to composite monotone inclusions involving parallel sums yields a new primal-dual splitting which is different from the existing methods. Connections to existing works are clearly stated. We also provide an application of the proposed method to the image denoising by the total variation.

关键词： Monotone inclusion Monotone operator Operator splitting Cocoercive forward-backward-forward method forward-backward algorithm Composite operator Duality Primal-dual algorithm

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Quadratic rates of asymptotic regularity for the Tikhonov-Mann iteration

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OPTIMIZATION METHODS & SOFTWARE 2022年第6期37卷 2225-2240页

作者： Cheval, Horaiu Leustean, Laureniu Univ Bucharest Fac Math & Comp Sci Res Ctr Log Optimizat & Secur LOS Dept Comp Sci Acad 14 Bucharest 010014 Romania Romanian Acad Simion Stoilow Inst Math Calea Grivitei 21 Bucharest 010702 Romania

In this paper, we compute quadratic rates of asymptotic regularity for the Tikhonov-Mann iteration in W-hyperbolic spaces. This iteration is an extension to a nonlinear setting of the modified Mann iteration defined recently by Bo, Csetnek and Meier in Hilbert spaces. Furthermore, we show that the Douglas-Rachford and forward-backward algorithms with Tikhonov regularization terms are special cases, in Hilbert spaces, of our Tikhonov-Mann iteration.

关键词： Mann iteration Tikhonov regularization rates of asymptotic regularity Douglas-Rachford algorithm forward-backward algorithm proof mining

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Convergence analysis and applications of the inertial algorithm solving inclusion problems

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APPLIED NUMERICAL MATHEMATICS 2022年 175卷 1-17页

作者： Tang, Yan Lin, Honghua Gibali, Aviv Cho, Yeol Je Chongqing Technol & Business Univ Sch Math & Stat Chongqing 400067 Peoples R China Sichuan Univ Coll Math Chengdu 610065 Peoples R China Southwest Univ Polit Sci & Law Business Sch Chongqing 401120 Peoples R China ORT Braude Coll Dept Math IL-2161002 Karmiel Israel Univ Haifa Ctr Math & Sci Computat Mt Carmel Haifa 3498838 Israel Gyeongsang Natl Univ Dept Math Educ Jinju 52828 South Korea China Med Univ Ctr Gen Educ Taichung 40402 Taiwan

Nonlinear operator theory is an important area of nonlinear functional analysis. This area encompasses diverse nonlinear problems in many areas of mathematics, the physical sciences and engineering such as monotone operator equations, fixed point problems and more. In this work we are concern with the problem of finding a common solution of a monotone operator equation and fixed point of a nonexpansive mapping in real Hilbert spaces. Derived from dynamical systems, a simple inertial forward-backward splitting method for solving the problem is presented and analyzed under mild and standard assumptions. Some numerical examples in real-world and comparisons with related works, illustrate the theoretical advantages as well the potential applicability of the proposed scheme. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Monotone operator equation Fixed point forward-backward algorithm Inertial technique Nonexpansive mapping

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A hidden Markov modeling approach for identifying tumor subclones in next-generation sequencing studies

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BIOSTATISTICS 2022年第1期23卷 69-82页

作者： Choo-Wosoba, Hyoyoung Albert, Paul S. Zhu, Bin NCI Biostat Branch Div Canc Epidemiol & Genet 9609 Med Ctr Dr Rockville MD 20850 USA

Allele-specific copy number alteration (ASCNA) analysis is for identifying copy number abnormalities in tumor cells. Unlike normal cells, tumor cells are heterogeneous as a combination of dominant and minor subclones with distinct copy number profiles. Estimating the clonal proportion and identifying mainclone and subclone genotypes across the genome are important for understanding tumor progression. Several ASCNA tools have recently been developed, but they have been limited to the identification of subclone regions, and not the genotype of subclones. In this article, we propose subHMM, a hidden Markov model-based approach that estimates both subclone region and region-specific subclone genotype and clonal proportion. We specify a hidden state variable representing the conglomeration of clonal genotype and subclone status. We propose a two-step algorithm for parameter estimation, where in the first step, a standard hidden Markov model with this conglomerated state variable is fit. Then, in the second step, region-specific estimates of the clonal proportions are obtained by maximizing region-specific pseudo-likelihoods. We apply subHMM to study renal cell carcinoma datasets in The Cancer Genome Atlas. In addition, we conduct simulation studies that show the good performance of the proposed approach. The R source code is available online at https://***/tools/analysis/subhmm. Expectation-Maximization algorithm;forward-backward algorithm;Somatic copy number alteration;Tumor subclones.

关键词： E-M algorithm forward-backward algorithm Somatic copy number alteration Tumor subclones

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Enhance the Voltage Profile and Minimize Power Loss of Radial Power System 10

Enhance the Voltage Profile and Minimize Power Loss of Radia...

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10th IEEE Uttar Pradesh Section International Conference on Electrical, Electronics and Computer Engineering, UPCON 2023

作者： Bhengra, Ivan Carol Rai, J.N. G. B. Pant Dseu Okhla-III Campus Delhi Skill and Entrepreneurship University New Delhi India Delhi Technological University Department of Electrical Engineering New Delhi India

ISBN: (纸本)9798350382471

In order to analyze the power flow in radial distribution systems, this paper suggests a backward/forward sweep method. High R/X ratios and radial structure characterize the distribution system as a result, the distribution system causes the Newton-Raphson and fast-decoupled methods to fail. One of the best methods for the load-flow analysis of the radial distribution system, the proposed method presents a load-flow study using the backward/forward sweep method. This method can be used to calculate voltage magnitudes at each bus node as well as power losses for each bus branch. The IEEE 33-bus Radial Distribution System has been used to test this method, and MATLAB has been used to produce efficient results. A small power plant known as distributed generation (DG) is attached to a distribution system load in order to enhance the voltage profile, voltage regulation, stability, lower power losses, and increase economic return. The DG can be placed in the best possible way to get the aforementioned benefits. The ideal DG placement and size are determined using a forward-backward algorithm. The algorithm has been put to the test on 33 bus test systems, and the outcomes have been contrasted with those of another evolutionary algorithm. The suggested algorithm with the DG unit operational produced the best results. © 2023 IEEE.

关键词： Breadth-first search (BFS) Distributed generation (DG) forward-backward algorithm IEEE 33 bus system IEEE 69 bus system

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