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Linear Regularity and Linear Convergence of projection-Based Methods for Solving Convex Feasibility Problems

APPLIED MATHEMATICS AND OPTIMIZATION 2018年第3期78卷 613-641页

作者： Zhao, Xiaopeng Ng, Kung Fu Li, Chong Yao, Jen-Chih Tianjin Polytech Univ Dept Math Tianjin 300387 Peoples R China Chinese Univ Hong Kong Dept Math Hong Kong Hong Kong Peoples R China Zhejiang Univ Sch Math Sci Hangzhou 310027 Zhejiang Peoples R China China Med Univ Ctr Gen Educ Taichung 40402 Taiwan Kaohsiung Med Univ Res Ctr Nonlinear Anal & Optimizat Kaohsiung 807 Taiwan

For a finite/infinite family of closed convex sets with nonempty intersection in Hilbert space, we consider the (bounded) linear regularity property and the linear convergence property of the projection-based methods for solving the convex feasibility problem. Several sufficient conditions are provided to ensure the bounded linear regularity in terms of the interior-point conditions and some finite codimension assumptions. A unified projection method, called algorithm B-EMOPP, for solving the convex feasibility problem is proposed, and by using the bounded linear regularity, the linear convergence results for this method are established under a new control strategy introduced here.

关键词： Convex feasibility problem Linear regularity projection algorithm

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Enforcing Intra-Regional Constraints in Tie-Line Scheduling: A projection-Based Framework

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IEEE TRANSACTIONS ON POWER SYSTEMS 2019年第6期34卷 4751-4761页

作者： Tan, Zhenfei Zhong, Haiwang Wang, Jianxiao Xia, Qing Kang, Chongqing Tsinghua Univ State Key Lab Power Syst Beijing 100084 Peoples R China Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China

Inter-regional power trading plays a crucial role in optimal resource utilization. However, intra-regional operation constraints are currently not well considered in practical implementation, which may lead to internal congestions and economic loss. In this paper, a non-iterative tie-line scheduling framework taking account of both intra- and inter-regional network constraints is proposed. Based on projection theory, admissible set of tie-line injections (ASTI) is defined as the allowable range of tie-line power injections that can be met by a regional system. Then, the ASTI is implemented in tie-line scheduling to ensure the feasibility of the tie-line schedule result for each region. Requirements for practical algorithms that calculate the ASTI in power system applications are analyzed, and a novel vertex-oriented projection algorithm is proposed to efficiently calculate the ASTI. Case studies based on several IEEE and Polish test systems verify the validity and efficiency of the proposed projection algorithm. Simulations based on a four-region system demonstrate the effectiveness of the proposed tie-line scheduling framework.

关键词： Tie-line scheduling congestion management admissible set projection algorithm economic dispatch

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Combining recursive projection and dynamic programming technique in multi UAVs formation anomaly detection

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INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL 2019年第1期31卷 53-61页

作者： Wang, Jian-Hong Jiang Univ Sci & Technol Sch Elect & Automat Ganzhou 341000 Peoples R China

To deal with the problem of anomaly detection in multi UAVs formation, and simplify the complexity of hypothesis testing or probability inequalities, the anomaly detection problem can be transformed to identify some unknown parameters process. To avoid a statistical description of measurement noise, a worthwhile alternative is the bounded noise characterisation. In the presence of bounded noise, the projection algorithm with dead zone and its modified form are proposed to identify the unknown parameters, such that the robustness of projection algorithm can be enhanced by increasing a dead zone. Furthermore, dynamic programming technique is introduced to balance the desire for lower present cost with the undesirability of high future cost in determining the anomaly detector, then the cost of collecting new observations and the higher probability of accepting the wrong hypothesis can be compensated. A numerical example illustrates the characteristics of the anomaly detection problem.

关键词： multi UAVs formation anomaly detection projection algorithm dynamic programming dead zone

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On the convergence of general projection methods for solving convex feasibility problems with applications to the inverse problem of image recovery

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OPTIMIZATION 2018年第9期67卷 1409-1427页

作者： Zhao, Xiaopeng Koebis, Markus Arthur Tianjin Polytech Univ Dept Math Tianjin Peoples R China Free Univ Berlin Dept Math & Comp Sci Berlin Germany

For an arbitrary family of closed convex sets with nonempty intersection in a Hilbert space, we consider the classical convex feasibility problem. We study the convergence property of the recently introduced unified projection algorithm B-EMOPP for solving this problem. For this, a new general control strategy is proposed, which we call the 'quasi-coercive control'. Under mild assumptions, we prove the convergence of B-EMOPP using these new control strategies as well as various other strategies. Several known results are extended and improved. The proposed algorithm is then applied to the inverse problem of image recovery.

关键词： Convex feasibility problem image recovery projection algorithm system of closed convex sets

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Modified three-term derivative-free projection method for solving nonlinear monotone equations with application

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NUMERICAL algorithmS 2023年第3期95卷 1459-1474页

作者： Abdullahi, Muhammad Abubakar, Auwal Bala Muangchoo, Kanikar Sule Lamido Univ Fac Nat & Appl Sci Dept Math Kafin Hausa Nigeria Bayero Univ Fac Phys Sci Dept Math Sci Numer Optimizat Res Grp Kano Nigeria Cent South Univ Sch Math & Stat HNP LAMA Changsha 410083 Hunan Peoples R China Sefako Makgatho Hlth Sci Univ Dept Math & Appl Math Ga Rankuwa Medunsa ZA-0204 Pretoria South Africa Rajamangala Univ Technol Phra Nakhon RMUTP Fac Sci & Technol Dept Math & Stat 1381 Pracharat 1 Rd Bangkok 10800 Thailand

In this paper, we propose a new modification of a three-term derivative-free projection algorithm for solving a system of monotone nonlinear equations. The global convergence was proved under some suitable conditions, and the search direction of the proposed algorithm satisfies the sufficient descent property. Numerical computations were presented to display the efficacy of the proposed algorithm compared to some existing algorithms. Moreover, the proposed algorithm is applied to solve problems of image recovery.

关键词： projection algorithm Monotone nonlinear equations Global convergence Image restoration

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Outer perturbations of a projection method and two approximation methods for the split equality problem

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OPTIMIZATION 2018年第9期67卷 1429-1446页

作者： Dong, Qiao-Li Li, Xiao-Huan He, Songnian Civil Aviat Univ China Tianjin Key Lab Adv Signal Proc Tianjin Peoples R China Civil Aviat Univ China Coll Sci Tianjin Peoples R China

In this article, we first present a projection method with outer perturbations for the split equality problem (SEP) and establish its weak convergence. Then combining the proposed projection method with the outer approximation method and Halpern iteration method, we introduce two approximation methods to solve the SEP, where the two closed convex sets are both level sets of convex functions. Finally, a preliminary experiment presented compares the approximation methods and a relaxed projection method.

关键词： Split equality problem projection algorithm relaxed projection algorithm Halpern iteration method outer perturbation outer approximation method

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ITERATIVE projection AND REFLECTION METHODS: THEORY AND PRACTICE

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BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY 2016年第1期94卷 175-176页

作者： Tam, Matthew K. Univ Gottingen Inst Numer & Angew Math D-37083 Gottingen Germany

The article focuses on the family of projection and reflection methods which form the basis for a class of iterative algorithms which can be used to solve the feasibility problem. It discusses the feasibility problem framework and fundamental projection-type algorithms, as well as the cyclic Douglas-Rachford method. Moreover, it focuses on a theory in the presence of convex constraint sets.

关键词： feasibility problem projection algorithm Douglas-Rachford algorithm projection operator reflection operator

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A projection-based Approach for Memory Leak Detection 42

A Projection-based Approach for Memory Leak Detection

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42nd Annual IEEE-Computer-Society Computers, Software and Applications (COMPSAC) Conference - Staying Smarter in a Smartening World

作者： Sun, Xiaohui Xu, Sihan Guo, Chenkai Xu, Jing Dong, Naipeng Ji, Xiujuan Zhang, Sen Nankai Univ Dept Binhai Tianjin Peoples R China Nankai Univ Dept Comp & Control Engn Tianjin Peoples R China Natl Univ Singapore Sch Comp Singapore Singapore

ISBN: (纸本)9781538626672

One of the major software safety issues is memory leak. Moreover, detecting memory leak vulnerabilities is challenging in static analysis. Existing static detection tools find bugs by collecting programs' information in the process of scanning source code. However, the current detection tools are weak in efficiency and accuracy, especially when the targeted program contains complex branches. This paper proposes a projection-based approach to detect memory leaks in C source code with complex control flows. According to the features of memory allocation and deallocation in C source code, this approach projects the original control flow graph of a program to a simpler one, and it reduces the analysis complexity. Besides, this paper implements a memory-leak detection tool-PML Checker, and evaluates the tool by comparing with three open-source static detection tools on both public benchmarks and study test cases. The experimental results show that PML Checker reports the most memory leak vulnerabilities among the four existing tools with complex control flows and complex data types, and PML Checker obtains higher efficiency and accuracy on public benchmarks.

关键词： memory leak projection algorithm static analysis

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Adaptive Position Control with Using a Smooth projection Adaptation Law for 2 DOF Flexible Link Robot Arm

Adaptive Position Control with Using a Smooth Projection Ada...

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Annual Conference of the Society-of-Instrument-and-Control-Engineers (SICE)

作者： Sawada, Masataka Itamiya, Keietsu Natl Def Acad Dept Elect & Elect Engn Yokosuka Kanagawa 2398686 Japan

ISBN: (纸本)9784907764401

We have already proposed high order tuner (HOT) which uses a smooth projection algorithm to ensure the positive definiteness of an estimated inertia matrix for realizing a stability and a good transient response of adaptive tracking control system based on [7] for a rigid link robot arm. Also, we proposed a HOT capable to constrain adjustable parameters into hyper-parallelogram region [8, 9]. In this paper, an adaptive control scheme for a 2 DOF flexible link robot arm is proposed. The controller is composed of an adaptation law using smooth projection algorithm [8, 9] and a control law based on dynamic certainty equivalent principle [7, 14]. The effectiveness of the proposed scheme is illustrated by a theoretical analysis and simple numerical simulation results.

关键词： adaptive control flexible link robot arm computed torque method projection algorithm

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An Efficient Method for Estimating Capability Curve of Virtual Power Plant

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CSEE Journal of Power and Energy Systems 2022年第3期8卷 780-788页

作者： Zhenfei Tan Haiwang Zhong Xuanyuan Wang Honghai Tang Department of Electrical Engineering State Key Laboratory of Power SystemsTsinghua UniversityBeijingChina Power exchange center State Grid Jibei Electric Power Co.LtdBeijingChina Beijing Power Exchange Center BeijingChina

To incorporate the operating constraints of a virtual power plant(VPP)in transmission-level operation and market clearing,the concept of the VPP capability curve(VPP-CC)is proposed which explicitly characterizes the allowable range of active and reactive power outputs of a VPP.A two-step projection-based calculation framework is proposed to approximate the VPP-CC by the convex hull of critical points on its *** output of the proposed algorithm is concise and can be easily incorporated in the existing system operation and market *** studies based on the IEEE 33 and 123 test feeders show the computational efficiency of the proposed method outperforms existing methods by 4~7 ***,many fewer inequalities are needed to depict the VPP-CC while achieving the comparative approximation accuracy compared to sampling-based methods,which will relieve the communication and computation burden.

关键词： Aggregation model capability curve optimal power flow projection algorithm virtual power plant

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