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On convergence analysis of a derivative-free trust region algorithm for constrained optimization with separable structure

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Science China Mathematics 2014年第6期57卷 1287-1302页

作者： XUE Dan SUN WenYu School of Mathematical Sciences Jiangsu Key Labratory for NSLSCSNanjing Normal University

In this paper,we propose a derivative-free trust region algorithm for constrained minimization problems with separable structure,where derivatives of the objective function are not available and cannot be directly *** each iteration,we construct a quadratic interpolation model of the objective function around the current *** new iterates are generated by minimizing the augmented Lagrangian function of this model over the trust *** filter technique is used to ensure the feasibility and optimality of the iterative *** convergence of the proposed algorithm is proved under some suitable assumptions.

关键词： constrained optimization derivative-free optimization multivariate interpolation separable op-timization global convergence

Hybrid data-driven framework for shale gas production performance analysis via game theory, machine learning, and optimization approaches

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Petroleum Science 2023年第1期20卷 277-294页

作者： Jin Meng Yu-Jie Zhou Tian-Rui Ye Yi-Tian Xiao Ya-Qiu Lu Ai-Wei Zheng Bang Liang Petroleum Exploration and Production Research Institute SINOPECBeijing100083PR China Jianghan Oilfield Company Research Institute of Exploration and DevelopmentSINOPECWuhan430223HubeiPR China

A comprehensive and precise analysis of shale gas production performance is crucial for evaluating resource potential,designing a field development plan,and making investment ***,quantitative analysis can be challenging because production performance is dominated by the complex interaction among a series of geological and engineering *** fact,each factor can be viewed as a player who makes cooperative contributions to the production payoff within the constraints of physical laws and *** by the idea,we propose a hybrid data-driven analysis framework in this study,where the contributions of dominant factors are quantitatively evaluated,the productions are precisely forecasted,and the development optimization suggestions are comprehensively *** specifically,game theory and machine learning models are coupled to determine the dominating geological and engineering *** Shapley value with definite physical meaning is employed to quantitatively measure the effects of individual factors.A multi-model-fused stacked model is trained for production forecast,which provides the basis for derivative-free optimization algorithms to optimize the development *** complete workflow is validated with actual production data collected from the Fuling shale gas field,Sichuan Basin,*** validation results show that the proposed procedure can draw rigorous conclusions with quantified evidence and thereby provide specific and reliable suggestions for development plan *** with traditional and experience-based approaches,the hybrid data-driven procedure is advanced in terms of both efficiency and accuracy.

关键词： Shale gas Production performance Data-driven Dominant factors Game theory Machine learning derivative-free optimization

Channel Knowledge Map(CKM)-Assisted Multi-UAV Wireless Network:CKM Construction and UAV Placement

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Journal of Communications and Information Networks 2023年第3期8卷 256-270页

作者： Haoyun Li Peiming Li Gaoyuan Cheng Jie Xu Junting Chen Yong Zeng School of Science and Engineering and the Future Network of Intelligence Institute(FNii)the Chinese University of Hong KongShenzhenShenzhen 518172China National Mobile Communications Research Laboratory and Frontiers Science Center for Mobile Information Communication and Security the Southeast UniversityNanjing 210096the Purple Mountain LaboratoriesNanjing 211111China

Channel knowledge map(CKM)has recently emerged as a viable new solution to facilitate the placement and trajectory optimization for unmanned aerial vehicle(UAV)communications,by exploiting the siteand location-specific radio propagation *** paper investigates a CKM-assisted multi-UAV wireless network,by focusing on the construction and utilization of CKMs for multi-UAV placement ***,we consider the CKM construction problem when data measurements for only a limited number of points are *** this end,we exploit a data-driven interpolation technique,namely the Kriging method,to construct CKMs to characterize the signal propagation ***,we study the multi-UAV placement optimization problem by utilizing the constructed CKMs,in which the multiple UAVs aim to optimize their placement locations to maximize the weighted sum rate with their respectively associated ground base stations(GBSs).However,the weighted sum rate function based on the CKMs is generally non-differentiable,which renders the conventional optimization techniques relying on function derivatives *** tackle this issue,we propose a novel iterative algorithm based on derivative-free optimization,in which a series of quadratic functions are iteratively constructed to approximate the objective function under a set of interpolation conditions,and accordingly,the UAVs’placement locations are updated by maximizing the approximate function subject to a trust region ***,numerical results are presented to validate the performance of the proposed *** is shown that the Kriging method can construct accurate CKMs for ***,the proposed derivative-free placement optimization design based on the Kriging-constructed CKMs achieves a weighted sum rate that is close to the optimal exhaustive search design based on ground-truth CKMs,but with much lower implementation *** addition,the proposed design is shown to significant

关键词： UAV communications CKM CKM construction UAV placement derivative-free optimization

AN AFFINE SCALING derivative-free TRUST REGION METHOD WITH INTERIOR BACKTRACKING TECHNIQUE FOR BOUNDED-CONSTRAINED NONLINEAR PROGRAMMING

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Journal of Systems Science & Complexity 2014年第3期27卷 537-564页

作者： GAO Jing ZHU Detong Department of Mathematics Shanghai Normal University

This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such a problem with polynomial interpolation models instead of the objective function in trust region subproblem. Combined with both trust region strategy and line search technique, at each iteration, the affine scaling derivative-free trust region subproblem generates a backtracking direction in order to obtain a new accepted interior feasible step. Global convergence and fast local convergence properties are established under some reasonable conditions. Some numerical results are also given to show the effectiveness of the proposed algorithm.

关键词： Affine scaling backtracking technique box constrains derivative-free optimization non-linear programming trust region method.

derivative-free reinforcement learning:a review

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Frontiers of Computer Science 2021年第6期15卷 75-93页

作者： Hong QIAN Yang YU National Key Laboratory for Novel Software Technology Nanjing UniversityNanjing 210023China

Reinforcement learning is about learning agent models that make the best sequential decisions in unknown *** an unknown environment,the agent needs to explore the environment while exploiting the collected information,which usually forms a sophisticated problem to ***-free optimization,meanwhile,is capable of solving sophisticated *** commonly uses a sampling-andupdating framework to iteratively improve the solution,where exploration and exploitation are also needed to be well ***,derivative-free optimization deals with a similar core issue as reinforcement learning,and has been introduced in reinforcement learning approaches,under the names of learning classifier systems and neuroevolution/evolutionary reinforcement *** such methods have been developed for decades,recently,derivative-free reinforcement learning exhibits attracting increasing ***,recent survey on this topic is still *** this article,we summarize methods of derivative-free reinforcement learning to date,and organize the methods in aspects including parameter updating,model selection,exploration,and parallel/distributed ***,we discuss some current limitations and possible future directions,hoping that this article could bring more attentions to this topic and serve as a catalyst for developing novel and efficient approaches.

关键词： reinforcement learning derivative-free optimization neuroevolution reinforcement learning neural architecture search

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基于简单模型函数的无导数信赖域方法

高等学校计算数学学报 2019年第2期41卷 176-192页

作者：席敏孙文瑜南京师范大学数学科学学院/江苏省大规模复杂系统数值模拟重点实验室广东外语外贸大学数学与统计学院

1引言考虑无约束最优化问题■f（x）,（1）其中f:R;→R是光滑的非线性函数,但函数f的导数无法计算或是需要耗费过多的计算量.这类优化问题广泛存在于科学计算、工程设计、生物化学等多个领域（见文献[1,7,11,14]）,备受人们的关注.例如... 详细信息

1引言考虑无约束最优化问题■f（x）,（1）其中f:R;→R是光滑的非线性函数,但函数f的导数无法计算或是需要耗费过多的计算量.这类优化问题广泛存在于科学计算、工程设计、生物化学等多个领域（见文献[1,7,11,14]）,备受人们的关注.例如,在某些问题中,目标函数的值是计算机模拟或物理

关键词： unconstrained optimization simple model derivative-free optimization trust-region method global convergence

Pattern Search Methods: Then and Now

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Pattern Search Methods: Then and Now

一个求解非线性方程组和最小二乘问题的过滤集无导数信赖域方法（英文）

中国运筹学会第七届学术交流会

作者： Wu Ting Department of Mathematics, Nanjing University, Nanjing, 210093

本文系统地阐述了求解无约束最优化问题的模式搜索方法,它的起始、发展和现状。特别是介绍了有关模式搜索的最新研究成果:基于正基和框架(frame)的模式搜索方法。并讨论了这类算法的收敛性。

关键词： direct search pattern search derivative-free optimization positive base

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高等学校计算数学学报 2021年第4期43卷 377-402页

作者：陈俊陈艳男孙海琳孙文瑜南京晓庄学院信息工程学院华南师范大学数学科学学院南京师范大学数学科学学院江苏省“大规模复杂系统数值模拟”重点实验室南京师范大学数学科学学院

We apply the filter technique to the model-based derivative-free trust region algorithm for solving nonlinear equations and nonlinear least-squares *** the work of Zhang et al.[SIAM ***.,20(2010),pp.3555-3576],we consider building the individual interpolation model for each component function in the nonlinear equations.A multidimensional filter,which is a list of n-tuples,is designed to potentially accept the trial point as the new iterate more *** far as we know,this is the first work to embed the filter mechanism into the model-based derivative-free *** suitable conditions,we establish the liminf-type and lim-type first-order global convergence results of the *** experiments show that the new algorithm is efficient.

关键词： derivative-free optimization trust region method filter technique multivariate polynomial interpolation global convergence