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Worst-case evaluation complexity of a quadratic penalty method for nonconvex optimization

OPTIMIZATION METHODS & SOFTWARE 2023年第4期38卷 781-803页

作者： Grapiglia, Geovani Nunes Catholic Univ Louvain ICTEAM INMA Louvain La Neuve Belgium Catholic Univ Louvain ICTEAM INMA Ave Georges Lemaitre 4-6 Louvain La Neuve B-1348 Belgium

This paper addresses the worst-case evaluation complexity of a version of the standard quadratic penalty method for smooth non convex optimization problems with constraints. The method analysed allows inexact solution of the subproblems and do not require prior knowledge of the Lipschitz constants related with the problem. When an approximate feasible point is used as starting point, ( ) it is shown that the referred method takes at most O log(s(-1) 0 e(-2)) outer iterations to generate an e-approximate KKT point, where s(0) is the first penalty parameter. For equality constrained problems, this bound yields to an evaluation complexity bound of O (e(-4)), when s0 = e(-2) and suitable first-order methods are used as inner solvers. complexity bound of O (e(-(P+1)/P)) is established when appropriFor problems having only linear equality constraints, an evaluation ate P-order methods (P = 2) are used as inner solvers. Illustrative numerical results are also presented and corroborate the theoretical predictions.

关键词： nonlinear programming quadratic penalty method worst-case complexity high-order methods

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Iterated dynamic neighborhood search for packing equal circles on a sphere

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COMPUTERS & OPERATIONS RESEARCH 2023年 151卷

作者： Lai, Xiangjing Yue, Dong Hao, Jin-Kao Glover, Fred Lu, Zhipeng Nanjing Univ Posts & Telecommun Inst Adv Technol Nanjing 210023 Peoples R China Univ Angers LERIA 2 Blvd Lavoisier F-49045 Angers France Entanglement Inc Boulder CO USA Huazhong Univ Sci & Technol Sch Comp Sci & Technol SMART Wuhan 430074 Peoples R China

In this work, we investigate the equal circle packing problem on a sphere (ECPOS), which consists in packing N equal non-overlapping circles on a unit sphere such that the radius of circles is maximized. The problem is of great interest in biology, engineering and operations research and thus has a rich research history both from theoretical and computational aspects. We propose from the point of view of computational research an effective iterated dynamic neighborhood search (IDNS) algorithm for the ECPOS problem. The algorithm includes a multiple-stage local optimization method, a general dynamic neighborhood search method and an adjustment method of the minimum distance between the points on the unit sphere. Extensive experiments are conducted with the proposed algorithm on 205 instances commonly used in the literature. Computational results show that the algorithm is highly effective by improving the best-known results for 42 instances and matching the best-known results for other 116 instances, while missing the best-known results for only 5 instances. For the remaining 42 instances, the best-known results are reported for the first time by the IDNS algorithm.

关键词： Circle packing Tammes problem Global optimization Metaheuristics nonlinear programming

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A Compound Gaussian Least Squares Algorithm and Unrolled Network for Linear Inverse Problems

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2023年 71卷 4303-4316页

作者： Lyons, Carter Raj, Raghu G. Cheney, Margaret US Naval Res Lab Washington DC 20375 USA Colorado State Univ Ft Collins CO 80523 USA

For solving linear inverse problems, particularly of the type that appears in tomographic imaging and compressive sensing, this paper develops two new approaches. The first approach is an iterative algorithm that minimizes a regularized least squares objective function where the regularization is based on a compound Gaussian prior distribution. The compound Gaussian prior subsumes many of the commonly used priors in image reconstruction, including those of sparsity-based approaches. The developed iterative algorithm gives rise to the paper's second new approach, which is a deep neural network that corresponds to an "unrolling" or "unfolding" of the iterative algorithm. Unrolled deep neural networks have interpretable layers and outperform standard deep learning methods. This paper includes a detailed computational theory that provides insight into the construction and performance of both algorithms. The conclusion is that both algorithms outperform other state-of-the-art approaches to tomographic image formation and compressive sensing, especially in the difficult regime of low training.

关键词： Artificial neural networks Training Tomography Signal reconstruction Signal processing algorithms Imaging Compounds Machine learning neural networks inverse problems nonlinear programming least squares methods

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Distributed Eco-Driving Control of a Platoon of Electric Vehicles Through Riccati Recursion

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2023年第3期24卷 3048-3063页

作者： Lacombe, Remi Gros, Sebastien Murgovski, Nikolce Kulcsar, Balazs Chalmers Univ Technol Dept Elect Engn S-41296 Gothenburg Sweden NTNU Dept Engn Cybernet N-7034 Trondheim Norway

This paper presents a distributed optimization procedure for the cooperative eco-driving control problem of a platoon of electric vehicles subject to safety and travel time constraints. Individual optimal trajectories are generated for each platoon member to account for heterogeneous vehicles and for the road slope. By rearranging the problem variables, the Riccati recursion can be applied along the chain-like structure of the platoon and be used to solve the problem by repeatedly transmitting information up and down the platoon. Since each vehicle is only responsible for its own part of the computations, the proposed control strategy is privacy-preserving and could therefore be deployed by any group of vehicles to form a platoon spontaneously while driving. The energy efficiency of this control strategy is evaluated in numerical experiments for platoons of electric trucks with different masses and rated motor powers.

关键词： Roads Force Vehicle dynamics Trajectory Indexes Electric vehicles Drag Distributed optimal control Riccati recursion platooning eco-driving electric vehicles nonlinear programming

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The opening workspace control strategy of a novel manipulator-driven emission source microscopy system

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ISA TRANSACTIONS 2023年 134卷 573-587页

作者： Liu, Xiaorui Li, Xian Su, Hang Zhao, Yuefang Ge, Shuzhi Sam Qingdao Univ Inst Future Automat Sch 308 Ningxia Rd Qingdao 266000 Shandong Peoples R China Qingdao ZDG New Energy Co Ltd 1 Jinye Rd Qingdao 266000 Shandong Peoples R China Politecn Milan Dipartimento Elettron Informaz & Bioingn I-20133 Milan Italy Shunhe Fangshu Inc Qingdao 266000 Shandong Peoples R China

Emission source microscopy (ESM) technique can be utilized for localization of electromagnetic interference sources in the electronic systems, but its accuracy is limited by the typical planar scanning mode. In order to increase the accuracy, this paper presents a novel cylinder-aperture ESM measurement system driven by 6-DOF manipulator, and investigated the control strategy to generate the maximum-area aperture and optimized scanning trajectory. Based on the multiple constraints of the cylinder-aperture ESM measurement, we proposes analyzing the impact of the constraints by steps. This can obtain the analytical solution of the manipulator workspace and support solving the maximum aperture area. Besides, a modified RRT*(Rapidly-exploring Random Trees) algorithm is addressed to optimize the manipulator trajectory. The simulation and tests have proven that this algorithm could obviously reduce the joint mutation and cumulative tracking error. In the experimental section, the near-field scanning (NFS) tests, planar-aperture ESM measurement and proposed cylinder-aperture ESM measurement were conducted to measure one benchmark emission source. The results have demonstrated that the cylinder-aperture ESM measurement has the best convergences on the radiation pattern of the emission source.(c) 2022 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： Electromagnetic interference(EMI) Emission source microscopy(ESM) Manipulator workspace Path planning optimization nonlinear programming

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Optimal transfer orbit design of spacecraft with finite thrust based on Legendre pseudospectral method

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART G-JOURNAL OF AEROSPACE ENGINEERING 2023年第8期237卷 1791-1797页

作者： Tu, Lianghui Wang, Yuhao Yan, Chao Yang, Yang Nanchang Hangkong Univ Sch Aircraft Engn Nanchang Peoples R China Nanchang Hangkong Univ Sch Aircraft Engn 696 Fenghe Nan Ave Nanchang 330063 Jiangxi Peoples R China

This article explores the application of the Legendre pseudospectral method to spacecraft orbital transfer with finite thrust optimization problem. Firstly, the model of the orbital transfer optimization control problem was established, while equations of motion were simplified based on some hypotheses. The performance was optimized to minimize the cumulative fuel consumption. The control variable was the thrust attack angle, and terminal state variable constraints included path angle, altitude, and velocity constraints. Then, the optimal control problem was transformed into a nonlinear programming problem (NLP) using the Legendre pseudospectral method. The dynamic optimization problem was transformed into a static parameter optimization problem. The state variables and control variables were selected as the optimal parameters at all collocation nodes. Lastly, the parameter optimization problem was solved using the SNOPT (Sparse nonlinear Optimizer) software package. The SNOPT software package shows high convergence for a nonlinear programming problem. During the simulation, it was noted that the Legendre pseudospectral method is not sensitive to orbital transfer initial conditions. It was also observed that the optimal solutions of the orbital transfer optimization problem are fairly good in robustness. Therefore, the Legendre pseudospectral method is a viable approach to the spacecraft orbital transfer with a finite thrust optimization problem. The orbit optimization method proposed in this paper can also provide reference and guidance for solving other interplanetary orbital transfer optimization problems.

关键词： Legendre pseudospectral method nonlinear programming finite thrust optimal orbital transfer spacecraft

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A Polynomial-Time Algorithm with Tight Error Bounds for Single-Period Unit Commitment Problem

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Journal of the Operations Research Society of China 2023年第1期11卷 1-28页

作者： Ruo-Tian Gao Shu-Cherng Fang Cheng Lu Wen-Xun Xing Big Data Center of State Grid Corporation of China Beijing 100053China Department of Industrial and System Engineering North Carolina State UniversityRaleigh 27695-7906USA School of Economics and Management North China Electric Power UniversityBeijing 102206China Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China

This paper proposes a Lagrangian dual-based polynomial-time approximation algorithm for solving the single-period unit commitment problem,which can be formulated as a mixed-integer quadratic programming problem and proven to be *** theoretical bounds for the absolute errors and relative errors of the approximate solutions generated by the proposed algorithm are *** results support the effectiveness and efficiency of the proposed algorithm for solving large-scale problems.

关键词： nonlinear programming Lagrangian dual Unit commitment problem Mixed-integer quadratic programming Convex relaxation

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An Accelerated Smoothing Newton Method with Cubic Convergence for Weighted Complementarity Problems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2023年第2期196卷 641-665页

作者： Tang, Jingyong Zhou, Jinchuan Zhang, Hongchao Xinyang Normal Univ Sch Math & Stat Xinyang 464000 Peoples R China Shandong Univ Technol Sch Math & Stat Zibo 255049 Peoples R China Louisiana State Univ Dept Math 303 Lockett Hall Baton Rouge LA 70803 USA

Smoothing Newton methods, which usually inherit local quadratic convergence rate, have been successfully applied to solve various mathematical programming problems. In this paper, we propose an accelerated smoothing Newton method (ASNM) for solving the weighted complementarity problem (wCP) by reformulating it as a system of nonlinear equations using a smoothing function. In spirit, when the iterates are close to the solution set of the nonlinear system, an additional approximate Newton step is computed by solving one of two possible linear systems formed by using previously calculated Jacobian information. When a Lipschitz continuous condition holds on the gradient of the smoothing function at two checking points, this additional approximate Newton step can be obtained with a much reduced computational cost. Hence, ASNM enjoys local cubic convergence rate but with computational cost only comparable to standard Newton's method at most iterations. Furthermore, a second-order nonmonotone line search is designed in ASNM to ensure global convergence. Our numerical experiments verify the local cubic convergence rate of ASNM and show that the acceleration techniques employed in ASNM can significantly improve the computational efficiency compared with some well-known benchmark smoothing Newton method.

关键词： nonlinear programming Weighted complementarity problem Accelerated smoothing Newton method Nonmonotone line search Cubic convergence

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Performance Assessment of Convex Low-Thrust Trajectory Optimization Methods

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JOURNAL OF SPACECRAFT AND ROCKETS 2023年第1期60卷 299-314页

作者： Hofmann, Christian Morelli, Andrea C. Topputo, Francesco Polytech Univ Milan Dept Aerosp Sci & Technol ViaLa Masa 34 I-20156 Milan Italy

Different discretization and trust-region methods are compared for the low-thrust fuel-optimal trajectory optimization problem using successive convex programming. In particular, the differential and integral formulations of the adaptive pseudospectral Legendre-Gauss-Radau method, an arbitrary-order Legendre-Gauss-Lobatto technique based on Hermite interpolation, and a first-order-hold discretization are considered. The number of discretization points and segments is varied. Moreover, two hard-trust-region methods and a soft-trust-region strategy are compared. It is briefly discussed whether these methods, if implemented on relevant hardware, would fulfill the general requirements for onboard guidance. A perturbed cubic interpolation and the propagation of the nonlinear dynamics are used to generate initial guesses of varying quality. Interplanetary transfers to a near-Earth asteroid, Venus, and asteroid Dionysus are chosen to assess the overall performance.

关键词： Trajectory Optimization Thrust Earth Asteroids nonlinear Dynamics Powered Descent Guidance Pseudospectral Methods nonlinear programming Sparse nonlinear Optimizer Polynomial Interpolation

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Joint mission planning and spectrum resources optimization for multi-UAV reconnaissance

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IET COMMUNICATIONS 2023年第3期17卷 324-335页

作者： Liao, Naiwen He, Panfeng Du, Yihang Zhang, Yu Chen, Yong Liang, Tao Natl Univ Def Technol Res Inst 63 Nanjing Peoples R China Army Engn Univ PLA Coll Commun Engn Nanjing Peoples R China

In this paper, the problem of mission planning and spectrum resource allocation for cooperative reconnaissance of ground targets with multiple unmanned aerial vehicles (UAVs) is studied. A joint mission planning and spectrum resource optimization algorithm for multi-UAVs is proposed to improve the information transmission rate by reusing the spectrum of existing users. The joint optimization problem is formulated as mixed-integer non-linear programming. The block coordinate descent (BCD) method is further applied to achieve the optimal strategies of mission planning, channel allocation, and power control. Specifically, an improved genetic algorithm (GA) combined with the successive convex approximation (SCA) is used to solve the sub-problem of mission planning. For the channel allocation sub-problem, an iterative convergence channel allocation algorithm is proposed. Numerical results show that the proposed algorithm can achieve a higher UAV transmission rate and better robustness than existing algorithms.

关键词： multiple unmanned aerial vehicles genetic algorithms joint optimization problem Optimisation techniques spectrum resource optimization algorithm improved genetic algorithm information transmission rate mixed-integer nonlinear programming convex programming Mobile robots iterative methods autonomous aerial vehicles Telerobotics joint mission planning Aerospace control higher UAV transmission rate Power and energy control multiUAVs iterative convergence channel allocation algorithm channel allocation spectrum resource allocation integer programming Telecommunication systems (energy utilisation) optimal strategies spectrum resources optimization Interpolation and function approximation (numerical analysis) multiUAV reconnaissance linear programming resource allocation power control optimisation UAVs nonlinear programming

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