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linear-quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equation with Lévy Process

Communications on Applied Mathematics and Computation 2022年第4期4卷 1386-1415页

作者： Hong Xiong Maoning Tang Qingxin Meng Department of Mathematics Zhejiang Normal UniversityJinhua 321004ZhejiangChina Department of Mathematical Sciences Huzhou UniversityHuzhou 313000ZhejiangChina

This paper investigates a linear-quadratic mean-field stochastic optimal control problem under both positive definite case and indefinite case where the controlled systems are mean-field stochastic differential equations driven by a Brownian motion and Teugels mar-tingales associated with Lévy processes.In either case,we obtain the optimality system for the optimal controls in open-loop form,and by means of a decoupling technique,we obtain the optimal controls in closed-loop form which can be represented by two Riccati differen-tial equations.Moreover,the solvability of the optimality system and the Riccati equations are also obtained under both positive definite case and indefinite case.

关键词： Mean-field Teugels martingales linear-quadratic Optimal control Riccati equations Feedback representation

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Turnpike Properties for Stochastic linear-quadratic Optimal Control Problems

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Chinese Annals of Mathematics,Series B 2022年第6期43卷 999-1022页

作者： Jingrui SUN Hanxiao WANG Jiongmin YONG Department of Mathematics Southern University of Science and TechnologyShenzhen 518055China Corresponding author.College of Mathematics and Statistics Shenzhen UniversityShenzhen 518060China Department of Mathematics University of Central FloridaOrlandoFL 32816USA

This paper analyzes the limiting behavior of stochastic linear-quadratic optimal control problems in finite time-horizon[0,T]as T→∞.The so-called turnpike properties are established for such problems,under stabilizability condition which is weaker than the controllability,normally imposed in the similar problem for ordinary differential systems.In dealing with the turnpike problem,a crucial issue is to determine the corresponding static optimization problem.Intuitively mimicking the deterministic situations,it seems to be natural to include both the drift and the diffusion expressions of the state equation to be zero as constraints in the static optimization problem.However,this would lead us to a wrong direction.It is found that the correct static problem should contain the diffusion as a part of the objective function,which reveals a deep feature of the stochastic turnpike problem.

关键词： Turnpike property Stochastic optimal control Static optimization linear-quadratic Stabilizability Riccati equation

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The challenges of precision radiotherapy technology to the traditional theory of radiobiology

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中华放射医学与防护杂志 2019年第8期39卷 563-571页

作者： Ma Shumei Liang Zhenzhen Chen Qiao Liu Rui Guo Yutian Liu Xiaodong School of Public Health and Management Wenzhou Medical University Wenzhou Zhejiang 325035 China MHC Key Lab of Radiation Biology School of Public Health Jilin University Changchun Jilin 130021 China Shenzhen Haibo Technology Co. Ltd. Shenzhen 518057 China

With the development of modern computing technology and medical physics,radiotherapy has made great progress.The theoretical basis of radiobiology seems to lag behind the clinical application of radiotherapy,which hampers the further improvement of treatment efficacy and the optimization of treatment modality.In this paper,some emerging challenges of precision radiotherapy technology to the traditional theory of radiobiology,such as radiosensitivity,dose-response curve and survival curve,linear-quadratic model,4Rs theory,as well as the interaction between cancer and microenvironment,radiation-induced second primary cancers(RISPC),will be discussed.The interplay between precision radiotherapy and traditional radiobiology theories will be addressed with the aim to potentially solve some of the challenging problems.

关键词： Precision radiotherapy Radiobiology linear-quadratic model Biological equivalent dose Radiosensitivity

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AN ITERATIVE METHOD FOR THE MINIMAX PROBLEM

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Numerical Mathematics A Journal of Chinese Universities(English Series) 1995年第2期4卷 237-239页

作者：祁立群孙文瑜 School of Mathematics University of New South WalesSydney 2052 Department of Mathematics Nanjing UniversityNanjing 210093PRC

In this paper a class of iterative methods for the minimax problem i; proposed.We present a sequence of the extented linear-quadratic programming (ELQP) problems as subproblems of the original minimal problem and solve the ELQP problem iteratively.The locally linear and su-perlinear convergence results of the algorithm are established.

关键词： minimax problem mathematical programming linear-quadratic programming convergence

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