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Augmented Lagrangian Methods for Convex Matrix Optimization Problems

Journal of the Operations Research Society of China 2022年第2期10卷 305-342页

作者： Ying Cui Chao Ding Xu-Dong Li Xin-Yuan Zhao Department of Industrial and Systems Engineering University of MinnesotaMinneapolis 55411USA Institute of Applied Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Data Science Fudan UniversityShanghai 200433China Shanghai Center for Mathematical Sciences Fudan UniversityShanghai 200433China College of Applied Sciences Beijing University of TechnologyBeijing 100124China

In this paper,we provide some gentle introductions to the recent advance in augmented Lagrangian methods for solving large-scale convex matrix optimization problems(cMOP).Specifically,we reviewed two types of sufficient conditions for ensuring the quadratic growth conditions of a class of constrained convex matrix optimization problems regularized by nonsmooth spectral *** a mild quadratic growth condition on the dual of cMOP,we further discussed the R-superlinear convergence of the Karush-Kuhn-Tucker(KKT)residuals of the sequence generated by the augmented Lagrangian methods(ALM)for solving convex matrix optimization *** details of the ALM for solving core convex matrix optimization problems are also provided.

关键词： Matrix optimization Spectral functions Quadratic growth conditions Metric subregularity Augmented Lagrangian methods Fast convergence rates Semismooth Newton methods

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Bio-heat transfer in skin tissue using fractional Weinbaum-Jiji model

Bio-heat transfer in skin tissue using fractional Weinbaum-J...

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2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023

作者： Essam, R. Elsaid, A. Zahra, W.K. Egypt-Japan University of Science and Technology Institute of Basic and Applied Sciences Alexandria Egypt Mansoura University Faculty of Engineering Mathematics and Engineering Physics Department Mansoura Egypt Tanta University Faculty of Engineering Engineering Physics and Mathematics Department Tanta Egypt

ISBN: (纸本)9798350321685

This study uses the Weinbaum-Jiji bioheat model to numerically simulate heat transfer through skin tissue that is exposed to a constant heat flux. The classical Weinbaum-Jiji equation is modified by including the Caputo fractional derivative in order to simulate the finite thermal propagation speed. The integration of the fractional calculus into the classical Weinbaum-Jiji equation facilitates the characterization of the flux-gradient relationship in terms of thermal time lag. This advancement extends the capabilities of the equation, allowing for a deeper understanding of the underlying physical processes. Using a discrete scheme, the problem is solved using a finite difference method for time and a finite element method for space. The results are compared to the previous efforts to model the problem, and good agreement is found in the rest of the case. The effects of the in-flow Péclet number and the effective thermal conductivity on the thermal profile along the tissues are illustrated. The variation of thermal profile along with the change in the inflow Péclet number reveals how vital is taking the vascular parameters into consideration. © 2023 IEEE.

关键词： Finite difference method

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Efficiency Assessment of an institute Through Parallel Network data Envelopment Analysis 11th

Efficiency Assessment of an Institute Through Parallel Netwo...

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11th International Conference on Soft Computing for Problem Solving, SocProS 2022

作者： Kumar, Atul Panwar, Ankita Pant, Millie Department of Applied Mathematics and Scientific Computing Indian Institute of Technology Roorkee Roorkee247667 India Mehta Family School of Data Science and Artificial Intelligence Indian Institute of Technology Roorkee Roorkee247667 India

ISBN: (纸本)9789811965241

Conventional data envelopment analysis (DEA) is a non-parametric approach to examine the efficiency of similar decision-making units (DMUs) as a whole system without considering its internal structure, i.e., the system is considered as a black box. Therefore, a network DEA (NDEA) is needed to study the internal structure of a system. By allowing for the measurement of individual components, an NDEA model can reveal inefficiencies that a traditional DEA ignores. In this study, we use the parallel network DEA to calculate the efficiency of a higher education institute with 19 decision-making units (DMUs) using two parallel processes (teaching and research) and compare it with the conventional DEA, CCR model through a numerical example. The main advantages of the parallel NDEA model are (i) to identify which DMUs are inefficient and make necessary adjustments, and (ii) the parallel DEA model has a lower efficiency score than the traditional DEA model. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Efficiency

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A Mathematical Model to Minimize the Total Cultivation Cost of Sugarcane 11th

A Mathematical Model to Minimize the Total Cultivation Cost ...

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11th International Conference on Soft Computing for Problem Solving, SocProS 2022

作者： Kumar, Sumit Pant, Millie Department of Applied Mathematics and Scientific Computing Indian Institute of Technology Roorkee Uttarakhand Roorkee India Mehta Family School for Data Science and Artificial Intelligence Indian Institute of Technology Roorkee Uttarakhand Roorkee India

ISBN: (纸本)9789811965241

In the present study, a non-linear mathematical model is proposed to minimize the total expenditure made on sugarcane cultivation. The objective here is to optimize the costs involved in transportation, cultivation, and management of the deterioration of sugarcane. The optimization tools used are Differential Evolution (DE) and Particle Swarm Optimization (PSO). Further, the model is validated by comparing the actual expenditure of sugarcane cultivation with results obtained by PSO and DE, which indicates that the application of optimization methods may help in reducing the expenditure made on sugarcane cultivation. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Deterioration

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Atmospheric Convection Model Based Digital Confidentiality Scheme

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Computers, Materials & Continua 2022年第6期71卷 4503-4522页

作者： Noor Munir Majid Khan Mohammad Mazyad Hazzazi Amer Aljaedi Sajjad Shaukat Jamal Iqtadar Hussain Department of Applied Mathematics and Statistics Institute of Space TechnologyIslamabadPakistan Department of Mathematics College of ScienceKing Khalid UniversityAbha61413Saudi Arabia College of Computing and Information Technology University of TabukTabuk71491Saudi Arabia Department of Mathematics Statistics and PhysicsQatar UniversityDoha2713Qatar

Nonlinear dynamics is a fascinating area that is intensely affecting a wide range of different disciplines of science and technology *** combination of different innovative topics of information security and high-speed computing has added new visions into the behavior of complex nonlinear dynamical systems which uncovered amazing results even in the least difficult *** generation of complex actions froma very simple dynamical method has a strong relation with information *** protection of digital content is one of the inescapable concerns of the digitally advanced ***,information plays an important role in everyday life and affects the surroundings *** digital contents consist of text,images,audio,and videos,*** to the vast usage of digital images in the number of social and web applications,its security is one of the biggest *** this work,we have offered an innovative image encryption technique based on present criteria of confusion and *** designed scheme comprises two major nonlinear dynamical *** have employed discrete fractional chaotic iterative maps to add confusion capability in our suggested algorithm and continuous chaotic Lorenz *** have verified our offered scheme by using statistical *** investigations under the statistical tests suggested that our proposed technique is quite reasonable for the security of digital data.

关键词： Lorenz atmospheric convection model fractional logistic map image encryption S-box

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On the Uncrossed Number of Graphs 32

On the Uncrossed Number of Graphs

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32nd International Symposium on Graph Drawing and Network Visualization, GD 2024

作者： Balko, Martin Hliněný, Petr Masařík, Tomáš Orthaber, Joachim Vogtenhuber, Birgit Wagner, Mirko H. Department of Applied Mathematics Faculty of Mathematics and Physics Charles University Prague Czech Republic Faculty of Informatics Masaryk University Brno Czech Republic Institute of Informatics Faculty of Mathematics Informatics and Mechanics University of Warsaw Poland Institute of Software Technology Graz University of Technology Austria Institute of Computer Science Osnabrück University Germany

ISBN: (纸本)9783959773430

Visualizing a graph G in the plane nicely, for example, without crossings, is unfortunately not always possible. To address this problem, Masařík and Hliněný [GD 2023] recently asked for each edge of G to be drawn without crossings while allowing multiple different drawings of G. More formally, a collection D of drawings of G is uncrossed if, for each edge e of G, there is a drawing in D such that e is uncrossed. The uncrossed number unc(G) of G is then the minimum number of drawings in some uncrossed collection of G. No exact values of the uncrossed numbers have been determined yet, not even for simple graph classes. In this paper, we provide the exact values for uncrossed numbers of complete and complete bipartite graphs, partly confirming and partly refuting a conjecture posed by Hliněný and Masařík [GD 2023]. We also present a strong general lower bound on unc(G) in terms of the number of vertices and edges of G. Moreover, we prove NP-hardness of the related problem of determining the edge crossing number of a graph G, which is the smallest number of edges of G taken over all drawings of G that participate in a crossing. This problem was posed as open by Schaefer in his book [Crossing Numbers of Graphs 2018]. © Martin Balko, Petr Hliněný, Tomáš Masařík, Joachim Orthaber, Birgit Vogtenhuber, and Mirko H. Wagner.

关键词： Graph theory

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Entropies of the Y-Junction Type Nanostructures

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Computer Modeling in Engineering & sciences 2023年第6期135卷 2665-2679页

作者： Ricai Luo Aisha Javed Muhammad Azeem Muhammad Kamran Jamil Hassan Raza Muhammad Yasir Ilyas School of Mathematics and Physics Hechi UniversityYizhou456300China Abdus Salam School of Mathematical Sciences Government College UniversityLahore54000Pakistan Department of Mathematics Riphah Institute of Computing and Applied SciencesRiphah International UniversityLahore54000Pakistan School of Mathematical Sciences College of Science and TechnologyWenzhou-Kean UniversityWenzhou325060China Department of Physics COMSATS University IslamabadLahore54000Pakistan

Recent research on nanostructures has demonstrated their importance and application in a variety of *** are used directly or indirectly in drug delivery systems,medicine and pharmaceuticals,biological sensors,photodetectors,transistors,optical and electronic devices,and so *** discovery of carbon nanotubes with Y-shaped junctions is motivated by the development of future advanced electronic *** of their interactionwithY-junctions,electronic switches,amplifiers,and three-terminal transistors are of particular *** is a concept that determines the uncertainty of a system or *** concepts are also used in biology,chemistry,and applied *** on the requirements,entropy in the form of a graph can be classified into several *** 1955,graph-based entropy was *** of the types of entropy is edgeweighted *** examined the abstract form of Y-shaped junctions in this *** edge-weight-based entropy formulas for the generic view of Y-shaped junctions were created,and some edge-weighted and topological index-based concepts for Y-shaped junctions were discussed in the present paper.

关键词： Y-shaped junctions three-terminal junctions nanostuctures entropy carbon nanotube

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The Semiconfined Harmonic Oscillator with a Position-Dependent Effective Mass: Exact Solution, Dynamical Symmetry Algebra and Quasiprobability Distribution Functions

The Semiconfined Harmonic Oscillator with a Position-Depen...

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International Workshop on Lie Theory and Its Applications in physics, LT 2023

作者： Jafarov, E.I. Nagiyev, S.M. Van der Jeugt, J. Institute of Physics Ministry of Science and Education Javid av. 131 BakuAZ1143 Azerbaijan Department of Applied Mathematics Computer Science and Statistics Faculty of Sciences Ghent University Krijgslaan 281-S9 Gent9000 Belgium

ISBN: (纸本)9789819764525

We present some details of the new model of the quantum harmonic oscillator that is semiconfined due to a specific change of its mass by position. We succeeded in solving exactly the Schrödinger equation corresponding to this model. Moreover, we found its dynamical symmetry algebra and could compute analytically its Kirkwood, Husimi and Wigner joint quasiprobability functions. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： Schrodinger equation

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用人工神经网络混合元启发式优化技术分析不可压缩黏性流体在收敛和发散通道中的流动:一种智能方法

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Journal of Central South University 2023年第12期30卷 4149-4167页

作者： ASLAM Muhammad Naeem RIAZ Arshad SHAUKAT Nadeem ALI Shahzad AKRAM Safia BHATTI M.M. Department of Physics and Applied Mathematics(DPAM) Pakistan Institute of Engineering&Applied SciencesNilore 45650IslamabadPakistan Center for Mathematical Sciences(CMS) Pakistan Institute of Engineering&Applied SciencesNilore 45650IslamabadPakistan Department of Mathematics Division of Science and TechnologyUniversity of EducationLahore 54770Pakistan School of Mathematics Minhaj UniversityLahorePakistan MCS National University of Sciences and TechnologyIslamabadPakistan College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China

本文采用人工神经网络(ANN)与进化算法(特别是阿基米德优化算法(AOA)和水循环算法(WCA)相结合的方法)对非线性磁流体动力学(MHD)的Jeffery-Hamel问题,特别是收敛和发散通道中的拉伸/收缩问题进行了数值研究。这种组合技术被称为ANN-AOA-... 详细信息

本文采用人工神经网络(ANN)与进化算法(特别是阿基米德优化算法(AOA)和水循环算法(WCA)相结合的方法)对非线性磁流体动力学(MHD)的Jeffery-Hamel问题,特别是收敛和发散通道中的拉伸/收缩问题进行了数值研究。这种组合技术被称为ANN-AOA-WCA。将基于复杂非线性磁流体动力学Jeffery-Hamel问题的偏微分方程转化为速度和温度的非线性常微分方程系统,我们建立了基于人工神经网络的适应度函数来求解非线性微分问题。随后,采用了一种新的AOA和WCA结合方法(AOAWCA)来优化基于神经网络的适应度函数,并确定了神经网络的最优权值和偏差。为了证明提出混合方法的有效性和多功能性,探索了一系列雷诺数、通道角和可拉伸边界值的MHD模型,从而开发了两种不同的情况。ANN-AOA-WCA的数值结果与参考解(NDSOLVE)非常接近,NDSOLVE与ANNAOA-WCA的绝对误差约为3.35×10^(−8),对可拉伸收敛和发散通道的理解特别关键。此外,为了验证ANN-AOA-WCA技术,我们对150多个独立运行进行了统计分析,以获得适应度值。

关键词：人工神经网络阿基米德优化水循环算法拉伸/收缩表面收敛或发散通道

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Mathematical Analysis of a Non-Smooth Mosquitoes Control Model

Mathematical Analysis of a Non-Smooth Mosquitoes Control Mod...

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2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023

作者： Fawzy, Doaa M. Arafa, Ayman A. Elsaid, A. Zahra, W.K. Institute of Basic and Applied Sciences Egypt Japan University of Science and Technology Alexandria Egypt Fayoum University Faculty of Engineering Department of Engineering Mathematics and Physics Fayoum Egypt Sohag University Faculty of Science Department of Mathematics Sohag Egypt Mansoura University Faculty of Engineering Department of Mathematics and Engineering Physics Mansoura Egypt Tanta University Faculty of Engineering Department of Engineering Physics and Mathematics Tanta Egypt

ISBN: (纸本)9798350321685

The sterilization method (SM) is a promising strategy for preventing the escalation of dengue fever, zika and malaria through controlling mosquitoes. A fractional-order SM non-smooth Filippov system with threshold policy control is proposed, which entails sterile mosquitoes releasing to control the population of wild mosquitoes. If the density of the wild population falls below a certain threshold, sterile release is prohibited. However, if the wild population exceeds the threshold, sterile mosquitoes are released. The dynamics of this model, including various types of equilibria existence and their stability, are investigated analytically and numerically. Sliding mode dynamics and pseudo-equilibrium are obtained by using the Filippov convex method;moreover, boundary node and boundary saddle bifurcations are discovered. © 2023 IEEE.

关键词： Bifurcation (mathematics)

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