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Convergence of the SQP method for quasilinear parabolic optimal control problems

OPTIMIZATION AND ENGINEERING 2021年第4期22卷 2039-2085页

作者： Hoppe, Fabian Neitzel, Ira Univ Bonn Inst Numer Simulat Endenicher Allee 19b D-53115 Bonn Germany

Based on the theoretical framework recently proposed by Bonifacius and Neitzel (Math Control Relat Fields 8(1):1-34, 2018. https://***/10.3934/mcrf.2018001) we discuss the sequential quadratic programming (SQP) method for the numerical solution of an optimal control problem governed by a quasilinear parabolic partial differential equation. Following well-known techniques, convergence of the method in appropriate function spaces is proven under some common technical restrictions. Particular attention is payed to how the second order sufficient conditions for the optimal control problem and the resulting L-2-local quadratic growth condition influence the notion of "locality" in the SQP method. Further, a new regularity result for the adjoint state, which is required during the convergence analysis, is proven. Numerical examples illustrate the theoretical results.

关键词： Optimal control Quasilinear parabolic partial differential equation sequential quadratic programming Convergence analysis

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Design of evolutionary optimized finite difference based numerical computing for dust density model of nonlinear Van-der Pol Mathieu's oscillatory systems

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MATHEMATICS AND COMPUTERS IN SIMULATION 2021年 181卷 444-470页

作者： Jadoon, Ihtesham Raja, Muhammad Asif Zahoor Junaid, Muhammad Ahmed, Ashfaq Rehman, Ata Ur Shoaib, Muhammad COMSATS Univ Islamabad Dept Elect & Comp Engn Wah Campus Rawalpindi Pakistan Natl Yunlin Univ Sci & Technol Future Technol Res Ctr 123 Univ RdSect 3 Touliu 64002 Yunlin Taiwan COMSATS Univ Islamabad Dept Elect & Comp Engn Campus Attock Attock Pakistan COMSATS Univ Islamabad Dept Math Campus Attock Attock Pakistan

In this study, a new evolutionary optimized finite difference based computing paradigm is presented for dynamical analysis of dust density model for the ensemble of electrical charges and dust particles represented with nonlinear oscillatory system based on hybridization of Van-der Pol and Mathieu equation (VDP-ME). Strength of accurate and effective discretization ability of finite difference method (FDM) is exploited to transform VDP-ME to equivalent nonlinear system of algebraic equations. The residual error based fitness function of the transformed model is constructed by the competency of approximation theory in mean square sense. The optimization of the residual error of the system through hybrid meta-heuristic computing paradigm GA-SQP;genetic algorithm (GA) for viable global search aided with rapid fine tuning of sequential quadratic programming (SQP). The proposed GA-SQP-FDM is applied on variants of dust density model of VDP-ME by varying the rate of charged dust grain production, as well as, loss and comparison of results with state of art numerical procedure established the worth of the scheme in terms of accuracy and convergence measures endorsed through statistical observations on large dataset. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Evolutionary computing Dusty plasma Finite difference method sequential quadratic programming Integrated computing

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A Novel IoT Application Recommendation System Using Metaheuristic Multi-Criteria Analysis

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Computer Systems Science & Engineering 2021年第5期37卷 149-158页

作者： Mohammed Hayder Kadhim Farhad Mardukhi Department of Computer Engineering and Information Technology Razi UniversityKermanshahIran

There are a variety of Internet of Things(IoT)applications that cover different aspects of daily *** of these applications has different criteria and sub-criteria,making it difficult for the user to *** requires an automated approach to select IoT applications by considering *** paper presents a novel recommendation system for presenting applications on the ***,using the analytic hierarchy process(AHP),a multi-layer architecture of the criteria and sub-criteria in IoT applications is *** architecture is used to evaluate and rank IoT *** a result,finding the weight of the criteria and subcriteria requires a metaheuristic *** this paper,a sequential quadratic programming algorithm is used to find the optimal weight of the criteria and sub-criteria *** the best of our knowledge,this is the first study to use an analysis of metaheuristic criteria and sub-criteria to design an IoT application recommendation *** evaluations and comparisons in the experimental results section show that the proposed method is a comprehensive and reliable model for the construction of an IoT applications recommendation system.

关键词： Internet of Things smart objects recommendation system multicriteria analysis sequential quadratic programming

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A Fast Temporal Decomposition Procedure for Long- Horizon Nonlinear Dynamic programming

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MATHEMATICS OF OPERATIONS RESEARCH 2023年第2期49卷 653-1302, C2页

作者： Na, Sen Anitescu, Mihai Kolar, Mladen Univ Calif Berkeley Int Comp Sci Inst Berkeley CA 94720 USA Univ Calif Berkeley Dept Stat Berkeley CA 94720 USA Argonne Natl Lab Math & Comp Sci Div Lemont IL 60439 USA Univ Chicago Booth Sch Business Chicago IL 60637 USA

We propose a fast temporal decomposition procedure for solving long-horizon nonlinear dynamic programs. The core of the procedure is sequential quadratic programming (SQP) that utilizes a differentiable exact augmented Lagrangian as the merit function. Within each SQP iteration, we approximately solve the Newton system using an overlapping temporal decomposition strategy. We show that the approximate search direction is still a descent direction of the augmented Lagrangian provided the overlap size and penalty parameters are suitably chosen, which allows us to establish the global convergence. Moreover, we show that a unit step size is accepted locally for the approximate search direction and further establish a uniform, local linear convergence over stages. This local convergence rate matches the rate of the recent Schwarz scheme (Na et al. 2022). However, the Schwarz scheme has to solve nonlinear subproblems to optimality in each iteration, whereas we only perform a single Newton step instead. Numerical experiments validate our theories and demonstrate the superiority of our method.

关键词： nonlinear dynamic programming temporal decomposition sequential quadratic programming augmented Lagrangian

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Resource Allocation for Millimeter-Wave Train-Ground Communications in High-Speed Railway Scenarios

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2021年第5期70卷 4823-4838页

作者： Zhang, Xiangfei Niu, Yong Mao, Shiwen Cai, Yunlong He, Ruisi Ai, Bo Zhong, Zhangdui Liu, Yiru Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing 100044 Peoples R China Beijing Jiaotong Univ Frontiers Sci Ctr Smart High Speed Railway Syst Beijing 100044 Peoples R China Southeast Univ Natl Mobile Commun Res Lab Nanjing 211189 Peoples R China Auburn Univ Dept Elect & Comp Engn Auburn AL 36849 USA Zhejiang Univ Dept ISEE Hangzhou 310027 Peoples R China Beijing Jiaotong Univ Beijing Engn Res Ctr High Speed Railway Broadband Beijing 100044 Peoples R China

With the development of wireless communication, higher requirements arise for train-ground wireless communications in high-speed railway (HSR) scenarios. The millimeter-wave (mm-wave) frequency band with rich spectrum resources can provide users in HSR scenarios with high performance broadband multimedia services, while the full-duplex (FD) technology has become mature. In this paper,we study train-ground communication system performance in HSR scenarios with mobile relays (MRs) mounted on rooftop of train and operating in the FD mode. We formulate a nonlinear programming problem to maximize network capacity by allocation of spectrum resources. Then, we develop a sequential quadratic programming (SQP) algorithm based on the Lagrange function to solve the bandwidth allocation optimization problem fortrack-side base station (BS) and MRs in this mm-wave train-ground communication system. Extensive simulation results demonstrate that the proposed SQP algorithm can effectively achieve high network capacity for train-ground communication in HSR scenarios while being robust to the residual self-interference (SI).

关键词： Wireless communication Communication systems Resource management Rail transportation Broadband communication Broadband antennas Wireless sensor networks Full-duplex communications sequential quadratic programming Train-ground communications high-speed railway Millimeter-wave communications Resource allocation

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A Combined Inverse Kinematics Algorithm Using FABRIK with Optimization

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JOURNAL OF INTELLIGENT & ROBOTIC SYSTEMS 2023年第4期108卷 62-62页

作者： Xu, Zichun Li, Yuntao Yang, Xiaohang Zhao, Zhiyuan Zhao, Jingdong Liu, Hong Harbin Inst Technol State Key Lab Robot & Syst Harbin 150001 Heilongjiang Peoples R China

Solving the inverse kinematics of redundant and hyper-redundant manipulators is more challenging because their kinematic redundancy leads to a more complicated mapping from end-effector pose to configuration space. A heuristic inverse kinematics solver, called Forward And Backward Reaching Inverse Kinematics (FABRIK), has been demonstrated to solve the inverse kinematics of complex chain systems with fast convergence and simple implementation. However, as the pose precision of the end-effector increases to a higher value, such as 10(-6), FABRIK converges slowly in some configurations and thus exhibits unstable convergence behavior. Hence, this paper presents a novel inverse kinematics algorithm that combines FABRIK and the sequential quadratic programming (SQP) algorithm, in which the joint angles deduced by FABRIK will be taken as the initial seed of the SQP algorithm to realize fast convergence. Meanwhile, a universal and non-trivial mapping from joint Cartesian positions to joint angles is included to enable the extension of FABRIK to redundant and hyper-redundant manipulators while retaining its simplicity. With the 10(-6) pose error constraint, quantitative tests on serial chain manipulators demonstrate that the combined algorithm outperforms FABRIK in terms of success rate and runtime. Meanwhile, some popular inverse kinematics algorithms are treated as benchmarks to compare with the combined algorithm. Finally, simulations using serial chain manipulators indicate the effectiveness of the combined algorithm on path tracking.

关键词： Inverse Kinematics Redundant Manipulators Hyper-Redundant Manipulators FABRIK sequential quadratic programming

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Neural-Based Predictive Control for Safe Autonomous Spacecraft Relative Maneuvers

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2021年第12期44卷 2303-2310页

作者： Silvestrini, Stefano Lavagna, Michele Polytech Univ Milan Dept Aerosp Sci & Technol Via La Masa 34 I-20156 Milan Italy

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A new benchmark optimization problem of adaptable difficulty: theoretical considerations and practical testing

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OPERATIONAL RESEARCH 2021年第1期21卷 231-250页

作者： Karpouzos, D. K. Katsifarakis, K. L. Aristotle Univ Thessaloniki Sch Agr Dept Hydraul Soil Sci & Agr Engn Thessaloniki 54124 Greece Aristotle Univ Thessaloniki Dept Civil Engn Div Hydraul & Environm Engn Thessaloniki 54124 Greece

In this paper, we present a new benchmark problem for testing both local and global optimization techniques. This problem is based on ideas from groundwater hydraulics and simple Euclidian geometry and has the following attractive features: (a) known values of the infinite global optima, which can be classified in a restricted number of sets, with known location in the search space (b) simple form and (c) quick computation of objective function values. Moreover, the number of local optima sets, their location in the search space and thus the respective values of the objective function can be easily determined by the user, without affecting the global optimum value. In this way, the difficulty of finding the global optimum can be changed from quite small to almost insurmountable, as demonstrated by applying five widely used optimization methods, namely genetic algorithms, sequential quadratic programming, simulated annealing, Knitro and branch and bound. Moreover, some observations on the different behavior of optimization methods are discussed.

关键词： Optimization Benchmark problem Adaptable difficulty Genetic algorithms sequential quadratic programming Simulated annealing Knitro Branch and bound

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Thermo-hydraulic condition optimization of large-scale complex district heating network: A case study of Tianjin

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ENERGY 2023年第1期266卷

作者： Zheng, Xuejing Shi, Zhiyuan Wang, Yaran Zhang, Huan Liu, Huzhen Tianjin Univ Sch Environm Sci & Engn Tianjin 300350 Peoples R China Tianjin Univ Key Lab Efficient Utilizat Low & Medium Grade Ener Minist Educ China Tianjin 300350 Peoples R China

District heating (DH) networks are indispensable infrastructure for space and domestic heating with high energy efficiency. As the structures of DH networks are gradually becoming complex, efficient and accurate simulation model for the operational optimization of the DH network is crucial. In this paper, an optimization method for the DH network operation is proposed. The method is based on the thermo-hydraulic coupled dynamic model, sequential quadratic programming (SQP) and particle swarm optimization (PSO), which is applied to a large-scale DH network in Tianjin, China. With the proposed method, 6.7%-11% energy consumption can be reduced, under the operation condition of 80%-100% design flow rate. The transmission and distribution cost can be reduced with an average of 6.2% at the outdoor temperature ranging from-5 to 5 degrees C.

关键词： District heating network Thermo-hydraulic coupled model sequential quadratic programming Particle swarm optimization Numerical simulation

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An SQP-based multiple shooting algorithm for large-scale PDE-constrained optimal control problems

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JOURNAL OF COMPUTATIONAL PHYSICS 2023年第1期477卷

作者： Fang, Liang Vandewalle, Stefan Meyers, Johan Katholieke Univ Leuven Dept Mech Engn Celestijnenlaan 300A Leuven Belgium Katholieke Univ Leuven Dept Comp Sci Celestijnenlaan 200A Leuven Belgium

Multiple shooting methods for solving optimal control problems have been developed rapidly in the past decades and are widely considered a promising direction to speed up the optimization process. Here we propose and analyze a new multiple shooting algorithm based on a sequential quadratic programming (SQP) method that is suitable for optimal control problems governed by large-scale time-dependent partial-differential equations (PDEs). We investigate the structure of the KKT matrix and solve the large-scale KKT system by a preconditioned conjugate gradient algorithm. A simplified block Schur complement preconditioner is proposed, that allows for the parallelization of the method in the time domain. The proposed algorithm is first validated for an optimal control problem constrained by the Nagumo equation. The results indicate that considerable accelerations can be achieved for multiple shooting approaches with appropriate starting guesses and scaling of the matching conditions. We further apply the proposed algorithm to a two-dimensional velocity tracking problem governed by the Navier-Stokes equations. We find algorithmic speed-ups of up to 12 versus single shooting on up to 50 shooting windows. We also compare results with earlier work that uses an augmented Lagrangian algorithm instead of SQP, showing better performance of the SQP method for most of the cases.(c) 2023 Elsevier Inc. All rights reserved.

关键词： Multiple shooting sequential quadratic programming PDE-constrained optimization

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