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Unified Representation of the Classical Ellipsoid Method

CYBERNETICS AND SYSTEMS ANALYSIS 2023年第5期59卷 784-793页

作者： Stetsyuk, P. I. Fischer, A. Khomiak, O. M. Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kiev Ukraine Tech Univ Dresden Inst Numer Math Dresden Germany Tech Univ Dresden Inst Numer Math Dresden Germany

A parametric version of the ellipsoid method with space scaling by a scalar parameter lambda > 0 is considered. For certain values of the parameter lambda, it is reduced to the well-known versions of the ellipsoid method, namely, the Shor, Khachiyan, Nemirovsky, and Yudin ones. The properties of two algorithmic implementations of the parameterized ellipsoid method are proved. The first algorithm is based on updating the asymmetric matrix B, and the second one updates the symmetric matrix H = BBT. The applications of the algorithms for solving convex programming problems and finding the saddle point of a convex-concave function are described.

关键词： ellipsoid method space dilation convex programming saddle point

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An Integrated Method for Robust Array Antenna Bounded Peak Sidelobe Level Synthesis Considering Mutual Coupling

An Integrated Method for Robust Array Antenna Bounded Peak S...

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IEEE International Conference on Microwaves, Communications, Antennas, Biomedical Engineering and Electronic Systems (COMCAS)

作者： Ding, Guangda Li, Peng Rocca, Paolo Xu, Wanye Xidian Univ Key Lab Elect Equipment Struct Design Minist Educ Xian 710071 Peoples R China Univ Trento ELEDIA UniTN ELEDIA Res Ctr Via Sommarive 9 I-38123 Trento Italy

ISBN: (纸本)9798350348194;9798350348187

This work proposes a linear array synthesis optimization method that maximizes the robustness against channel calibration and/or mutual coupling (MC) errors. The circular interval analysis (CIA) method is used to describe the interval power patterns of array antennas with errors (channel calibration and MC), and then the radiation power pattern is optimized using the analysis tools of convex programming (CP) methods, to satisfy the user-defined mask constraints for the main lobe width and the sidelobe level, while obtaining the optimal excitation weights for the antenna elements. A set of representative examples is reported to demonstrate the effectiveness and robustness of the proposed method. Finally, the proposed method is applied to a preliminary robust design of a spherical conformal array antenna with calibration errors, laying the foundation for future research on conformal array antenna synthesis.

关键词： Synthesis optimization mutual coupling channel calibration circular interval analysis convex programming spherical conformal array antenna

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Autonomous parafoil precision landing using convex real-time optimized guidance and control

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CEAS SPACE JOURNAL 2023年第2期15卷 371-384页

作者： Leeman, Antoine Preda, Valentin Huertas, Irene Bennani, Samir European Space Agcy Directorate Technol Engn & Qual GNC AOCS 1 NL-2201 AZ Noordwijk Netherlands European Space Agcy Directorate Technol Engn & Qual Pointing Div 1 NL-2201 AZ Noordwijk Netherlands Swiss Fed Inst Technol Inst Dynam Syst & Control Zurich Switzerland

To overcome the limitations of current parafoil precision landing capabilities, an efficient real-time convex optimized guidance and control strategy is presented. The parafoil guidance problem is non-convex in essence and it can be solved with a sequence of convex problems, each of those converging in polynomial time to a feasible solution of the approximated original problem. Our approach shows reliable and fast numerical convergence through in-flight recalculation of time of flight and a new optimal trajectory to cope with time-varying dynamics. The efficiency of our strategy is demonstrated via a comparative analysis of the existing X-38 in-flight demonstrated guidance and control system. Exhaustive Monte Carlo simulations show performance improvements of about one order of magnitude. The concept proposed is simple, yet general, as it scales to any atmospheric parafoil landing system and allows efficient implementation relying only on the turn rate saturation information for the parafoil model.

关键词： Parafoil convex programming Guidance and control Landing Real time Trajectory optimization Sequential convex programming

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Necessary Optimality Conditions for Vector Reverse convex Minimization Problems via a Conjugate Duality

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VIETNAM JOURNAL OF MATHEMATICS 2024年第1期52卷 265-282页

作者： Keraoui, Houda Aboussoror, Abdelmalek Univ Cadi Ayyad Lab Modelisat Syst Complexes ENSA BP 575Ave Abdelkrim Khattabi Marrakech 40000 Morocco Univ Cadi Ayyad Fac Sci Semlalia Blvd Prince My AbdellahBP 2390 Marrakech 40000 Morocco

In this paper, we are concerned with a vector reverse convex minimization problem (P). For such a problem, by means of the so-called Fenchel-Lagrange duality, we provide nec-essary optimality conditions for proper efficiency in the sense of Geoffrion. This duality is used after a decomposition of problem (P) into a family of convex vector minimization sub-problems and scalarization of these subproblems. The optimality conditions are expressed in terms of subdifferentials and normal cones in the sense of convex analysis. The obtained results are new in the literature of vector reverse convex programming. Moreover, some of them extend with improvement some similar results given in the literature, from the scalar case to the vectorial one.

关键词： Multiobjective programming Reverse convex programming convex programming Optimality conditions Primary Secondary

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Fast Model Predictive Control of Input-Affine Systems: Application to the Hindmarsh-Rose Neuron Model 4

Fast Model Predictive Control of Input-Affine Systems: Appli...

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4th Modeling, Estimation, and Control Conference (MECC)

作者： Grancharova, Alexandra Xie, Junhong Olaru, Sorin Univ Chem Technol & Met Dept Ind Automat Bul Kl Ohridski 8 Sofia 1756 Bulgaria Univ Paris Saclay Cent Supelec Lab Signals & Syst CNRSUniv Paris Sud Gif Sur Yvette France

The paper presents a low complexity nonlinear MPC design for the class of constrained input-affine systems. Essentially, it builds on the idea of adding a contractive constraint in the NMPC problem formulation, which would ensure the closed-loop system stability when using a small prediction horizon. In particular, the one-step ahead NMPC problem with contractive constraint is considered and an approach to obtain an efficient online solution of the associated convex quadratically constrained quadratic programming problem is developed. The proposed technique is shown to be effective for embedded convex NMPC of input-affine systems, since it will reduce the computational complexity of the online NMPC and simplify the software and hardware implementation. The methodological developments are illustrated with simulations on the Hindmarsh-Rose neuron model. Copyright (C) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0/)

关键词： Predictive control Nonlinear systems Constraints convex programming Computational complexity

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The radius of robust feasibility of uncertain mathematical programs: A Survey and recent developments*

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第3期296卷 749-763页

作者： Goberna, M. A. Jeyakumar, V. Li, G. Vicente-Perez, J. Univ Alicante Dept Math Alicante 03080 Spain Univ New South Wales Dept Appl Math Sydney NSW 2052 Australia

The radius of robust feasibility provides a numerical value for the largest possible uncertainty set that guarantees feasibility of a robust counterpart of a mathematical program with uncertain constraints. The objective of this review of the state-of-the-art in this field is to present this useful tool of robust opti-mization to its potential users and to avoid undesirable overlapping of research works on the topic as those we have recently detected. In this paper we overview the existing literature on the radius of ro-bust feasibility in continuous and mixed-integer linearly constrained programs, linearly constrained semi-infinite programs, convexly constrained programs, and conic linearly constrained programs. We also ana-lyze the connection between the radius of robust feasibility and the distance to ill-posedness for different types of uncertain mathematical programs. (c) 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://***/licenses/by-nc-nd/4.0/ )

关键词： Robustness and sensitivity analysis Radius of robust feasibility Linear programming Integer programming convex programming Semi-infinite programming Conic linear programming Distance to ill-posedness

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Discrete Choice Prox-Functions on the Simplex

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MATHEMATICS OF OPERATIONS RESEARCH 2022年第1期47卷 485-507页

作者： Mueller, David Nesterov, Yurii Shikhman, Vladimir Tech Univ Chemnitz Dept Math D-09126 Chemnitz Germany Catholic Univ Louvain Ctr Operat Res & Econometr B-1348 Louvain La Neuve Belgium

We derive new prox-functions on the simplex from additive random utility models of discrete choice. They are convex conjugates of the corresponding surplus functions. In particular, we explicitly derive the convexity parameter of discrete choice prox-functions associated with generalized extreme value models, and specifically with generalized nested logit models. Incorporated into subgradient schemes, discrete choice prox-functions lead to a probabilistic interpretations of the iteration steps. As illustration, we discuss an economic application of discrete choice prox-functions in consumer theory. The dual averaging scheme from convex programming adjusts demand within a consumption cycle.

关键词： convex programming prox-function discrete choice additive random utility models dual averaging consumption cycle

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Safe Learning in Nonlinear Model Predictive Control 6

Safe Learning in Nonlinear Model Predictive Control

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6th Annual Learning for Dynamics and Control Conference

作者： Buerger, Johannes Cannon, Mark Doff-Sotta, Martin BMW Grp Munich Germany Univ Oxford Dept Engn Sci Oxford England

A robust Model Predictive Control algorithm is proposed for learning-based control with model represented by an affine combination of basis functions. The online optimization is formulated as a sequence of convex programming problems derived by linearizing concave components of the dynamic model. A tube-based approach ensures satisfaction of constraints on control variables and model states while avoiding conservative bounds on linearization errors. The linear dependence of the model on unknown parameters is exploited to allow safe online parameter adaptation. The resulting algorithm is recursively feasible and provides closed loop stability and performance guarantees. Numerical examples are provided to illustrate the approach.

关键词： Nonlinear predictive control convex programming adaptive control learning control

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Data-Driven Adaptive Compensation in Droop-Operated Low-Voltage Microgrids 18

Data-Driven Adaptive Compensation in Droop-Operated Low-Volt...

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18th International Conference on Probabilistic Methods Applied to Power Systems (PMAPS)

作者： Trickett, Lucas Voon, Liming Watson, Jeremy Univ Canterbury Dept Elect & Comp Engn Christchurch New Zealand

ISBN: (纸本)9798350372793;9798350372786

AC microgrids typically use droop-operated gridforming inverters for voltage and frequency regulation as this allows stabilisation of the microgrid without communication. However, in cases with very low X/R line ratios, there is greater coupling between real and reactive power and stability issues can occur. This paper proposes the use of an adaptive data-driven compensator which operates in conjunction with droop-control. The proposed data-driven control uses an LQR formulation for improved performance, and is updated in real-time according to developed criteria in order to adapt to network changes. We demonstrate improved stability regions via a large-scale MATLAB/Simulink study of a two-inverter test system where the line and load parameters are varied randomly.

关键词： data-driven control convex programming grid-forming inverters microgrid control low-voltage

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Fast multidimensional dictionary learning algorithms and their application in 3D inverse synthetic aperture radar image restoration and noise reduction

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IET RADAR SONAR AND NAVIGATION 2022年第9期16卷 1484-1502页

作者： Mehrpooya, Ali Nazari, Milad Abbasi, Zahra Karbasi, Seyed M. Nayebi, Mohammad M. Bastani, Mohammad H. Sharif Univ Technol Dept Elect Engn Tehran Iran Malek Ashtar Univ Technol Dept Elect Engn Tehran Iran

By generalising dictionary learning (DL) algorithms to multidimensional (MD) mode and using them in applications where signals are inherently multidimensional, such as in three-dimensional (3D) inverse synthetic aperture radar (ISAR) imaging, it is possible to achieve much higher speed and less computational complexity. In this study, the formulation of the multidimensional dictionary learning (MDDL) problem is expressed and two algorithms are proposed to solve it. The first one is based on the method of optimum directions (MOD) algorithm for 1D dictionary learning (1DDL), which uses alternating minimisation and gradient projection approach. As the MDDL problem is non-convex, the second algorithm approximates the non-convex objective with a new jointly convex function and efficiently solves it. As an application, we use the proposed methods to restore and denoise the ISAR image. Numerical experiments highlight that the proposed algorithms, in addition to reducing the computational complexity and the amount of required memory, also entail less training data for learning the dictionary, and enjoy higher convergence speed in comparison to their one-dimensional (1D) counterparts. Specifically, convergence speed of MD algorithms, depending on the size of the training data, is up to at least 10.7 times faster than the equivalent 1DDL algorithm. According to the simulation results, the SNR value achieved by the proposed algorithms is higher than the case where we use the 3D-IFFT for image reconstruction and the case of fixed dictionaries, by approximately 12 and 4 dB, respectively.

关键词： gradient projection approach optimum directions algorithm jointly convex function multidimensional mode ISAR image 3D inverse synthetic aperture radar image restoration convex programming MDDL problem three-dimensional inverse synthetic aperture radar imaging noise reduction image restoration radar imaging fast multidimensional dictionary learning algorithms training data MD algorithms equivalent 1DDL algorithm one dimensional counterparts fixed dictionaries multidimensional dictionary learning problem gradient methods computational complexity synthetic aperture radar image denoising nonconvex objective image reconstruction

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