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Existence and Uniqueness of Positive Solutions to Nonlinear Systems of Equations With M-Type Functions

IEEE ACCESS 2020年 8卷 84153-84161页

作者： Bai, Xueli Tianjin Univ Sch Math Tianjin 300350 Peoples R China

This paper considers the existence and uniqueness of positive solutions to a class of nonlinear systems of equations, which has wide applications in fluid mechanics and electrical circuit theory. In this paper, we define a new class of functions, called -type function, and then, we show some good properties of -type function as well as the relationship between this kind of functions and other kinds of functions. In particular, by fully exploiting the properties of -type function, we present that under a reasonable condition, the nonlinear system of equations with an -type function, which can be seen as a generalization of the multilinear system with a nonsingular -tensor, and a positive right-hand side vector has a unique positive solution. Meanwhile, for this class of problems, we give a preliminary and simple algorithm framework. What is more, under an additional assumption, we illustrate the feasibility of using Newton step when improving the original iteration algorithm to obtain better convergence. Numerical experiments show the stability and efficiency of the proposed algorithms.

关键词： iteration algorithm M-type function Newton step nonlinear system of equations off-diagonally antitone unique positive solution

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An effective fixed-base model with classical normal modes for soil-structure interaction systems

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SOIL DYNAMICS AND EARTHQUAKE ENGINEERING 2001年第8期21卷 689-698页

作者： Wu, WH Chen, CY Natl Yunlin Univ Sci & Technol Dept Construct Engn Yuanlin 640 Taiwan

To simplify the analysis of soil-structure interaction systems, various fixed-base models have recently been proposed by the author to efficiently represent the SSI system and have been shown to have good accuracy. However, the modified mass and damping matrices of these models do not hold the properties of symmetry and orthogonality. Difficulties may consequently be induced for these models in applying conventional computer codes to carry out dynamic analysis. In the present paper, this problem is further explored to establish a fixed-base model possessing classical normal modes. Formulated in the modal space, this fixed-base model is constructed through applying an iteration algorithm to incorporate the Gram-Schmidt orthogonalization process. The convergent real orthogonal mode vectors, natural frequencies, and modal damping ratios are directly determined for this model. It is demonstrated with a numerical example that this new fixed-base model retains excellent accuracy. Accordingly, the complicated SSI systems can be directly analyzed using conventional computer codes for structural dynamics with the fixed-base model developed in this study. (C) 2001 Elsevier Science Ltd. All rights reserved.

关键词： soil-structure interaction fixed-base model classical normal mode modal space Gram-Schmidt orthogonalization process iteration algorithm

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Convergence theorems of common fixed points for a finite family of Lipschitz pseudocontractions in Banach spaces

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2008年第10期68卷 2977-2983页

作者： Zhou, Haiyun N China Elect Power Univ Inst Nonlinear Anal Baoding 071003 Peoples R China

In this paper, we continue to study weak convergence problems for the implicit iteration process for a finite family of Lipschitzian continous pseudocontractions in general Banach spaces. The results presented in this paper improve and extend the corresponding ones of Xu and Ori [H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mapphigs, Number. Funct. Anal. Optim. 22 (2001) 767-773], Osilike [M.O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl. 294 (2004) 73-81], Chen et al. [R. Chen, ***, H.Y. Zhou, Convergence theorems for implicit iteration process for a finite family of continous pseudocontractive mappings, J. Math. Anal. Appl. 314 (2006) 701-709] and others. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： Lipschitz pseudocontraction iteration algorithm convergence theorem

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Trace ratio criterion for multi-view discriminant analysis

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APPLIED INTELLIGENCE 2022年第13期52卷 14679-14692页

作者： Shi, Mei Li, Zhihui Zhao, Xiaowei Xu, Pengfei Liu, Baoying Guo, Jun Northwest Univ Sch Informat Sci & Technol Xian 710127 Peoples R China Qilu Univ Technol Shandong Artificial Intelligence Inst Shandong Acad Sci Jinan Peoples R China Northwestern Polytech Univ Sch Comp Sci Xian 710072 Shaanxi Peoples R China Northwestern Polytech Univ Sch Artificial Intelligence Opt & Elect iOPEN Xian 710072 Shaanxi Peoples R China Shaanxi Int Joint Res Ctr Battery free Internet T Xian 710127 Peoples R China

Learning from heterogeneous views, termed multi-view learning (MvL), is a significant yet challenging problem in computer vision. Many existing MvL methods apply the two-view principle to multi-view scenarios, but this pairwise approach is neither efficient nor optimal and leads to poor performance. Then some multi-view discriminant analysis methods are proposed by simultaneously considering the intra-view and inter-view correlation across multiple views, and the final form of these methods is a trace ratio (TR) problem. Traditionally, the solution to the TR problem is normally approximated by generalized eigenvalue decomposition, failing to obtain the global optimum solution. Although some iterative algorithms are proposed to directly solve the TR problem, these methods are not rigorous in the absence of theoretical discussion. To overcome these weaknesses, we propose a novel supervised MvL model called Trace Ratio Criterion for Multi-view Discriminant Analysis (TRCMvDA) by jointly learning multiple view-specific linear transforms. In particular, we propose an iterative algorithm based on the Newton-Raphson method to directly solve the TR problem and successfully avoid deviation from the original objectives. In addition, we prove the convergence and effectiveness of our algorithm theoretically and empirically. Experiments conducted on five universal datasets reveal that our TRCMvDA achieves better performance than state-of-the-art methods.

关键词： Trace ratio criterion Common space projection Multi-view discriminant analysis iteration algorithm

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To exploit the flexibility of TSO-DSO interaction: A coordinated transmission robust planning and distribution stochastic reinforcement solution

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ENERGY REPORTS 2023年 9卷 27-36页

作者： Liu, Jia Zhang, Libo Liu, Kaicheng Tang, Zao Zeng, Peter Pingliang Li, Yalou China Elect Power Res Inst Natl Key Lab Power Grid Secur & Energy Conservat Beijing 100192 Peoples R China Hangzhou Dianzi Univ Dept Automat Hangzhou 310018 Peoples R China

With the penetration of distributed energy resources into distribution systems, the power exchange between distribution and transmission systems becomes more coupled and flexible. The technical and economy performance of the expansion approach could be improved with the consideration of TSO-DSO interconnection and interaction. This paper presents a hierarchical planning framework for distribution stochastic and transmission robust optimization in a coordinated manner. Source-network-load uncertainties in transmission network are formulated using uncertain set while source-demand uncertainties in distribution networks are described with a set of representative scenarios. An integrated solution procedure, including column and constraint generation and iteration algorithm, is proposed to determine the transmission robust and distribution stochastic expansion schemes. Simulation carried out on a transmission network with three distribution networks validates the high performance of the formulated problem compared with the existing isolated expansion approach. (c) 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： Robust transmission expansion Stochastic distribution reinforcement TSO-DSO interaction Uncertainties iteration algorithm

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Optimal dividend problems with a risk probability criterion

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NAVAL RESEARCH LOGISTICS 2022年第3期69卷 421-430页

作者： Wen, Xin Guo, Xianping Xia, Li Sun Yat Sen Univ Sch Math Guangzhou Peoples R China Sun Yat Sen Univ Sch Business Guangzhou Peoples R China Sun Yat Sen Univ Guangdong Prov Key Lab Computat Sci Guangzhou Peoples R China

This paper considers a discrete time optimal dividend payout problem with a risk probability criterion. Different from the expected discounted dividends that are widely studied in the existing literature, our emphasis is the risk probability that an insurance company's total discounted dividend fails to reach a given dividend goal by the time of ruin. We aim to find an optimal dividend policy to minimize such risk probability. More precisely, we establish a general model for optimal dividend problems based on a Markov decision process with varying discount factors and a probability criterion. The associated optimality equation and the existence of optimal policies under the probability criterion are investigated. For a special case with independently identically distributed incomes, we further characterize the properties of optimal value functions and the structures of optimal dividend policies. A value iteration-type algorithm for computing value functions and optimal policies is developed. The convergence and error bound analyses of the algorithm are also derived. Finally, an optimal dividend policy in a concrete example is presented to demonstrate our main results.

关键词： iteration algorithm Markov decision process optimal dividend problem risk probability criterion structures of optimal dividend policies

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To the Construction of Mathematical Models for Quasilinear Discretely Observed Distributed Space-Time Systems

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JOURNAL OF AUTOMATION AND INFORMATION SCIENCES 2011年第8期43卷 19-32页

作者： Stoyan, V. A. Golodiuk, D. A. Kiev Natl Taras Shevchenko Univ Kiev Ukraine

The paper is focused on the dynamics of distributed space-time process which is discretely observed at the input and continuously observed at the output. The algorithms of linear, nonlinear and approximate identification of integral model of this process are proposed. The conditions of accuracy and uniqueness of existence of approximate solution are determined.

关键词： dynamical system distributed space-time process space-time domain iteration algorithm

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A NOTE ON SIMULTANEOUS ROOTFINDING FOR ALGEBRAIC, EXPONENTIAL, AND TRIGONOMETRIC POLYNOMIALS

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 1994年第7期27卷 7-14页

作者： CARSTENSEN, C Institut f&uuml r Angewandte Mathematik Universit&auml t Hannover Welfengarten 1 D-30167 Hannover Germany

A common derivation and convergence analysis is presented for two methods for the simultaneous computation of all the zeros of an algebraic, exponential, or trigonometric polynomial. The analysis is performed considering a certain class of generalized polynomials which allow a factorization in terms of translations of a function q(t) such that Lagrangian-like interpolation is exact. The methods were already known for algebraic polynomials (q(t) = t) but new for exponential (q(t) = sinh(t/2)) and trigonometric polynomials (q(t) = sin(t/2)). Using the properties q(0) = 0, q'(0) not-equal 0, and q''(0) = 0, we prove the local convergence of the methods presented in this note. The algorithms only require the evaluation of the generalized polynomial at certain points but no derivatives or coefficients. Numerical examples are included.

关键词： iteration algorithm SIMULTANEOUS ROOTFINDING GENERALIZED POLYNOMIALS

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Block Sparse Signals Recovery algorithm for Distributed Compressed Sensing Reconstruction

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JOURNAL OF INFORMATION PROCESSING SYSTEMS 2019年第2期15卷 410-421页

作者： Chen, Xingyi Zhang, Yujie Qi, Rui China Univ Geosci Fac Informat Engn Wuhan Hubei Peoples R China China Univ Geosci Sch Math & Phys Wuhan Hubei Peoples R China Naval Univ Engn Sch Sci Wuhan Hubei Peoples R China China Univ Geosci Hubei Subsurface Multiscale Imaging Key Lab Wuhan Hubei Peoples R China

Distributed compressed sensing (DCS) states that we can recover the sparse signals from very few linear measurements. Various studies about DCS have been carried out recently. In many practical applications, there is no prior information except for standard sparsity on signals. The typical example is the sparse signals have block-sparse structures whose non-zero coefficients occurring in clusters, while the cluster pattern is usually unavailable as the prior information. To discuss this issue, a new algorithm, called backtracking-based adaptive orthogonal matching pursuit for block distributed compressed sensing (DCSBBAOMP), is proposed. In contrast to existing block methods which consider the single-channel signal reconstruction, the DCSBBAOMP resorts to the multi-channel signals reconstruction. Moreover, this algorithm is an iterative approach, which consists of forward selection and backward removal stages in each iteration. An advantage of this method is that perfect reconstruction performance can be achieved without prior information on the block-sparsity structure. Numerical experiments are provided to illustrate the desirable performance of the proposed method.

关键词： Block Sparse Signals Compressed Sensing Distributed Compressed Sensing iteration algorithm

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Solution algorithm of a quasi-Lambert's problem with fixed flight-direction angle constraint

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CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY 2011年第4期109卷 409-427页

作者： Luo, Qinqin Meng, Zhanfeng Han, Chao Beijing Univ Aeronaut & Astronaut Beijing 100191 Peoples R China China Acad Space Technol Beijing 100094 Peoples R China

A two-point boundary value problem of the Kepler orbit similar to Lambert's problem is proposed. The problem is to find a Kepler orbit that will travel through the initial and final points in a specified flight time given the radial distances of the two points and the flight-direction angle at the initial point. The Kepler orbits that meet the geometric constraints are parameterized via the universal variable z introduced by Bate. The formula for flight time of the orbits is derived. The admissible interval of the universal variable and the variation pattern of the flight time are explored intensively. A numerical iteration algorithm based on the analytical results is presented to solve the problem. A large number of randomly generated examples are used to test the reliability and efficiency of the algorithm.

关键词： Two-point boundary value problem Quasi-Lambert's problem Flight-direction angle Universal Variable iteration algorithm

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