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Numerical shape reconstruction approaches for solving free boundary inverse problem for the p-Laplacian operator

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2025年 463卷

作者： Chakib, Abdelkrim Khalil, Ibrahim Sultan Moulay Slimane Univ Fac Sci & Tech Appl Math Team AMT Beni Mellal Morocco

In this paper, we develop efficient numerical shape reconstruction approaches for solving the Bernoulli free boundary inverse problem, constrained by a nonlinear elliptic problem for the p-Laplacian operator. In this framework, let us first mention that, to our best knowledge, the numerical resolution of this problem has never been investigated in previous works, for different values of p > 1. So, we propose here a shape optimal design formulation of this inverse free boundary problem and address its shape sensitivity analysis using both distributed and boundary types of Eulerian derivatives. Then, we develop two numerical gradient shape optimization processes for solving this shape optimization problem, based on the distributed and the boundary shape derivative formulas, performed with the Picard iterations procedure and the finite element Galerkin discretization, for solving the auxiliary nonlinear boundary value problem involving p-Laplacian operator. Finally, several numerical results are presented in two and three dimensions, showing that the shape optimization gradient process based on the distributed Eulerian derivative is more efficient than the one based on the classical boundary shape derivative, in solving this kind of problems.

关键词： Shape optimization Bernoulli problem p-Laplacian operator Shape derivative Distributed formula Boundary formula gradient algorithm Finite elements approximation

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Network-level aircraft trajectory planning via multi-agent deep reinforcement learning: Balancing climate considerations and operational manageability

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 271卷

作者： Baneshi, Fateme Cerezo-Magana, Maria Soler, Manuel Univ Carlos III Madrid Dept Aerosp Engn Ave Univ 30 Leganes 28911 Madrid Spain

Optimizing flight trajectories emerges as a viable strategy to mitigate the non-CO2 climate impacts of aviation. However, integrating individually optimized trajectories into the air traffic management system poses operational challenges, notably in terms of traffic safety and complexity. This paper presents a novel cooperative decision-making framework employing multi-agent deep reinforcement learning to plan operationally feasible climate-friendly routes from the perspective of the air traffic management system. The proposed strategy leverages the twin delayed deep deterministic policy gradient (TD3) algorithm to adjust flight trajectories during the planning phase to resolve the potential conflicts associated with climate-optimal trajectories. Addressing the scalability issue inherent in multi-agent environments, we derive a unique policy applicable to arbitrary numbers of concurrently operating aircraft. To handle the non-stationarity of the environment, fully observable critic networks are employed, providing comprehensive situational awareness for each agent during training. The effectiveness of the proposed approach is validated by comparing it against three algorithms and evaluating the derived policy across multiple sets of climate-optimal trajectories over European airspace. The results demonstrate that our framework can effectively mitigate aviation's climate impact while maintaining operational feasibility. Restricting decision space to only speed changes, up to 80% climate impact reduction is achievable while decreasing potential conflicts by 10% compared to standard business-as-usual trajectories. Notably, without applying the proposed method, obtaining similar climate impact mitigation leads to a substantial increase in the number of conflicts. Enhancing the proposed framework by incorporating additional decision variables such as lateral path and altitude adjustments, as well as other ATM performance indicators relevant to the flight planning phase,

关键词： Aviation climate impact Aircraft trajectory planning Multi-agent deep reinforcement learning Conflict resolution Air traffic management system Twin delayed deep deterministic policy gradient algorithm

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Synthesis of gradient algorithms with the Minimum Systematic Error for Estimating Directional Fields

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OPTOELECTRONICS INSTRUMENTATION AND DATA PROCESSING 2010年第1期46卷 1-8页

作者： Gruzman, I. S. Karpushin, V. B. Novosibirsk State Tech Univ Pr Karla Marksa 20 Novosibirsk 630092 Russia

A method is proposed for constructing noise-resistant mask differentiating filters minimizing systematic errors in estimating directional fields by a gradient algorithm. A comparative analysis of the accuracy of gradient algorithms was performed by computer modeling It is shown that a decrease in the systematic error leads to a considerable increase in the accuracy of directional field estimation

关键词： directional field gradient algorithm mask differentiating filter

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Distributed subgradient algorithm for multi-agent optimization with directed communication topology

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IFAC-PapersOnLine 2015年第28期48卷 863-868页

作者： YIN, Yanhui LIU, Zhongxin CHEN, Zengqiang College of Computer and Control Engineering Nankai University Tianjin300071 China Tianjin Key Laboratory of Intelligent Robotics Nankai University Tianjin300071 China College of Science Civil Aviation University of China Tianjin300300 China

This paper studies a distributed subgradient algorithm in directed graphs. In contrast to previous work the problem is considered when the weighted adjacency matrices are not doubly stochastic. First the paper shows that an agreement can be reached in general directed graphs, but the global optimal function may not be minimized. Then some knowledge about homogeneous Markov chains is used to analyze the transition matrices and a new update rule is proposed to ensure that the a lgorithm converges to the optimal set for the case when the topology of graphs is fixed and known to all agents. For switching topology the paper establishes the relationship between the optimal results and the limit vector sequence. The paper provides explicit proof for the results and stimulation research validates the effectiveness. © 2015

关键词： Topology Chains Directed graphs Graphic methods Markov processes Multi agent systems Stochastic systems Adjacency matrices Communication topologies Distributed optimization Doubly stochastic Homogeneous markov chains Sub gradient algorithm Switching topology Transition matrices

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Convergence of gradient method for training ridge polynomial neural network

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NEURAL COMPUTING & APPLICATIONS 2013年第1-sup期22卷 S333-S339页

作者： Yu, Xin Deng, Fei Guangxi Univ Sch Comp Elect & Informat Nanning 530004 Peoples R China

The ridge polynomial neural network is one of the most popular higher-order neural networks, which has the powerful capability of approximating reasonable functions while avoiding the combinatorial increase in the number of weights required. In this paper, we study the convergence of gradient method with batch updating rule for ridge polynomial neural network, and a monotonicity theorem and two convergence theorems (including a weak convergence and a strong convergence) are proved. The experimental results demonstrate that the proposed theorems are valid.

关键词： Ridge polynomial neural network gradient algorithm Monotonicity Convergence

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Shape gradient of the dissipated energy functional in shape optimization for the viscous incompressible flow

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APPLIED NUMERICAL MATHEMATICS 2008年第11期58卷 1720-1741页

作者： Gao, Zhiming Ma, Yichen Xi An Jiao Tong Univ Sch Sci Xian 710049 Shaanxi Peoples R China Xi An Jiao Tong Univ Sch Sci Shaanxi 710049 Peoples R China

This paper is concerned with I numerical simulation of, shape optimization ill a two-dimensional viscous incompressible flow governed by Navier-Stokes equations with mixed boundary conditions containing the pressure. The minimization problem of total dissipated energy was established in the fluid domain. We derive the structures of continuous Shape gradient of the cost functional by using the differentiability of a minimax formulation involving a Lagrange functional with a function space parametrization technique. Finally it gradient type algorithm is effectively used for our problem. (C) 2007 IMACS. Published by Elsevier B.N. All rights reserved.

关键词： Shape gradient Shape optimization Minimax principle gradient algorithm Navier-Stokes equations

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Relative gradient based algorithms for general joint diagonalization of complex matrices

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MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING 2016年第1期27卷 275-293页

作者： Trainini, Tual Moreau, Eric Aix Marseille Univ CNRS ENSAM LSISUMR 7296 F-13397 Marseille France Univ Toulon & Var CNRS LSIS UMR 7296 F-83957 La Garde France

This article deals with the problem of joint diagonalization of hermitian and/or complex symmetric matrices. Within the framework of gradient algorithms, we develop various algorithms which are based on different levels of approximation of the classical diagonalization criterion. The algorithms are based on a multiplicative update and on the derivation of an optimal step-size. One of the algorithms is a generalization of DOMUNG to the complex case. Finally, in the blind source separation context, computer simulations illustrate the relative performances of some proposed algorithms in comparison to the true gradient one.

关键词： gradient algorithm Joint diagonalization Independent component analysis Blind source separation

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Combined inverse and gradient iterative learning control: performance, monotonicity, robustness and non-minimum-phase zeros

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2014年第3期24卷 406-431页

作者： Owens, David H. Chu, Bing Univ Sheffield Dept Automat Control & Syst Engn Sheffield S1 3JD S Yorkshire England Univ Southampton Sch Elect & Comp Sci Southampton SO17 1BJ Hants England Inst Italiano Tecnol Dept Adv Robot I-16163 Genoa Italy

Based on recent papers that have demonstrated that robust iterative learning control can be based on parameter optimization using either the inverse plant or gradient concepts, this paper presents a unification of these ideas for discrete-time systems that not only retains the convergence properties and the robustness properties derived in previous papers but also permits the inclusion of filters in the input update formula and a detailed analysis of the effect of non-minimum-phase dynamics on algorithm performance in terms of a plateauing' or flat-lining' effect in the error norm evolution. Although the analysis is in the time domain, the robustness conditions are expressed as frequency domain inequalities. The special case of a version of the inverse algorithm that can be used to construct a robust stable anti-causal inverse non-minimum-phase plant is presented and analysed in detail. Copyright (c) 2012 John Wiley & Sons, Ltd.

关键词： iterative learning control parameter optimization inverse systems gradient algorithm optimization

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Tracking properties of a gradient-based second-order adaptive IIR notch filter with constrained poles and zeros

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2002年第4期50卷 878-888页

作者： Xiao, YG Takeshita, Y Shida, K Dainippon Printing Informat Syst Inc Tokyo Japan Saga Univ Fac Sci & Engn Saga 840 Japan

gradient-type adaptive IIR notch filters have many attractive merits for various real-life applications since they require a small number of computations and yet demonstrate practical performance. However, it is generally quite difficult to assess their performance analytically. Their tracking properties, in particular, have not yet been investigated. In this paper, the tracking performance of a plain gradient (PG) algorithm is analyzed in detail for a second-order adaptive IIR notch filter with constrained poles and zeros, which takes a linear chirp signal as its input. First, two sets of difference equations for the frequency tracking error and mean square error (MSE) are established in the sense of convergence in the mean and convergence in the mean square, respectively. Closed-form expressions for the asymptotic tracking error and MSE are then derived from these difference equations. An optimum step-size parameter for the algorithm is also evaluated based on the minimization of the asymptotic tracking error or the tracking MSE. It is discovered that the asymptotic tracking error may be driven to zero for a positive chirp rate by selecting a proper step size, which is an interesting property for a real-valued adaptive filtering algorithm. Extensive simulations are performed to support the analytical findings.

关键词： adaptive IIR notch filtering frequency tracking gradient algorithm tracking error tracking MSE

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Convergence of gradient method with penalty for Ridge Polynomial neural network

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NEUROCOMPUTING 2012年 97卷 405-409页

作者： Yu, Xin Chen, Qingfeng Guangxi Univ Sch Comp Elect & Informat Nanning 53004 Peoples R China

In this paper, a penalty term is added to the conventional error function to improve the generalization of the Ridge Polynomial neural network. In order to choose appropriate learning parameters, we propose a monotonicity theorem and two convergence theorems including a weak convergence and a strong convergence for the synchronous gradient method with penalty for the neural network. The experimental results of the function approximation problem illustrate the above theoretical results are valid. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Ridge Polynomial neural network gradient algorithm Monotonicity Convergence

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