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Indefinite Abstract Splines with a quadratic Constraint

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2020年第1期186卷 209-225页

作者： Gonzalez Zerbo, Santiago Maestripieri, Alejandra Martinez Peria, Francisco Consejo Nacl Invest Cient & Tecn CONICET Inst Argentino Matemat Alberto P Calderon IAM Buenos Aires DF Argentina Univ Buenos Aires Fac Ingn Buenos Aires DF Argentina Univ Nacl La Plata Ctr Matemat La Plata CMaLP La Plata Argentina

We study an extension to Krein spaces of the abstract interpolating spline problem in Hilbert spaces, introduced by M. Atteia. This is a quadratically constrained quadratic programming problem, where the objective function is not convex, while the equality constraint is sign indefinite. We characterize the existence of solutions and, if there are any, we describe the set of solutions as the union of a family of affine manifolds parallel to a fixed subspace, which depend on the original data.

关键词： Abstract splines Krein spaces quadratically constrained quadratic programming Linear quadratic regulator

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Robust Transceiver Design in the Presence of Eclipsing Loss for Spectrally Dense Environments

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IEEE SYSTEMS JOURNAL 2021年第3期15卷 4334-4345页

作者： Yao, Yu Wu, Lenan Liu, Haitao East China Jiaotong Univ Sch Informat Engn Nanchang 330013 Jiangxi Peoples R China Southeast Univ Sch Informat Sci & Engn Nanjing 210096 Peoples R China East China Jiaotong Univ Sch Mechatron & Vehicle Engn Nanchang 330013 Jiangxi Peoples R China

Radar system design for the detection of targets with unknown actual range in spectrally crowded environments is a challenge due to increasing demands for spectrum and the possibly experienced echo eclipsing. Assuming unknown target echo delay, this article deals with robust joint design of the radar code and receive filter bank guaranteeing spectral compatibility with the surrounding electromagnetic radiators. The average signal-to-interference-plus-noise ratio (SINR) at the output of the filter bank is considered as the performance measure to optimize under both similarity and spectral compatibility constraints on the radar code. Through an appropriate reformulation of the resulting nonconvex optimization problem, we devise an alternate optimization algorithm, which sequentially improves the average SINR and converges to a point fulfilling the Karush-Kuhn-Tucker (KKT) conditions of the design problem. Each iteration of the algorithm involves both a convex and a hidden convex optimization problem, which can be solved via the rank-1 decomposition procedure. Finally, the performance is assessed by studying the tradeoff among the SINR, spectral shape, and autocorrelation. Numerical results reveal that the new method has better flexibility and robustness compared to several counterparts, which are presented in open literature.

关键词： Radar Interference Signal to noise ratio Optimization Linear matrix inequalities Robustness Transceivers Eclipsing loss filter bank design joint transmit-receive optimization quadratically constrained quadratic programming spectral coexistence

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On Convex Hulls of Epigraphs of QCQPs 21st

On Convex Hulls of Epigraphs of QCQPs

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21st International Conference on Integer programming and Combinatorial Optimization (IPCO)

作者： Wang, Alex L. Kilinc-Karzan, Fatma Carnegie Mellon Univ Pittsburgh PA 15213 USA

ISBN: (纸本)9783030457716;9783030457709

quadratically constrained quadratic programs (QCQPs) are a fundamental class of optimization problems well-known to be NP-hard in general. In this paper we study sufficient conditions for a convex hull result that immediately implies that the standard semidefinite program (SDP) relaxation of a QCQP is tight. We begin by outlining a general framework for proving such sufficient conditions. Then using this framework, we show that the convex hull result holds whenever the quadratic eigenvalue multiplicity, a parameter capturing the amount of symmetry present in a given problem, is large enough. Our results also imply new sufficient conditions for the tightness (as well as convex hull exactness) of a second order cone program relaxation of simultaneously diagonalizable QCQPs.

关键词： quadratically constrained quadratic programming Semidefinite program Convex hull Relaxation Lagrange function

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Uncertainty Propagation with Semidefinite programming 54

Uncertainty Propagation with Semidefinite Programming

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54th IEEE Conference on Decision and Control (CDC)

作者： Choi, Hyungjin Seiler, Peter J. Dhople, Sairaj V. Univ Minnesota Dept Elect & Comp Engn Minneapolis MN 55455 USA Univ Minnesota Dept Aerosp Engn & Mech Minneapolis MN 55455 USA

ISBN: (纸本)9781479978861

This paper outlines an optimization-based method to estimate the reach set of a system while acknowledging unknown-but-bounded input and parametric uncertainty in the underlying dynamical model. The approach is grounded in a second-order Taylor-series expansion of the system's state variables along the solution trajectories as a function of the uncertain elements. Subsequently, over the time horizon of interest, quadratically constrained quadratic Programs (QCQPs) are formulated to estimate maximum and minimum bounds on the state variables to recover the reach set. To contend with the nonconvexity of the QCQPs, Lagrangian relaxations are leveraged to formulate Semidefinite Programs (SDPs) that provide guaranteed bounds to the solutions of the QCQPs. Applications of the method to quantify the impact of uncertain power injections in power-system dynamic models are demonstrated with numerical examples.

关键词： quadratically constrained quadratic programming Reachability analysis Semidefinite programming Sensitivity analysis Uncertainty propagation

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A Comparison Between QCQP-relaxation Methods to Determine a Lower Bound on a Small Antenna Q-factor 13

A Comparison Between QCQP-relaxation Methods to Determine a ...

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13th European Conference on Antennas and Propagation (EuCAP)

作者： Jonsson, B. L. G. KTH Royal Inst Technol EECS Stockholm Sweden

ISBN: (纸本)9788890701887

quadratically constrained quadratic programming (QCQP) can be used to determine the best Q-factor for small antennas with constraints on the antenna efficiency. Constraints on the total directivity and a given front-to-back ratio can also be expressed as QCQP. Such problems are non-convex and hence challenging to solve. Their solution gives the best Q-factor available for any antenna within the considered volume. Thus, solutions to this type of problems provide a tool, which before the design can predict the best possible antenna performance within a given volume of a device. It is hence important to investigate methods to solve this class of QCQP problems. In this paper we compare and investigate two relaxation methods, the Lagrangian dual and semidefinite relaxation, to estimate lower bounds on the Q-factor. The former method is here reduced to solving a generalized eigenvalue-problem. Properties of the different relaxation methods are illustrated and compared. We focus in this paper on the Q-factor and its relation to efficiency, as expressed by the dissipation factor. However, these tools also apply to a larger class of problems including constraints on the directivity and other far-field conditions.

关键词： antenna Q-factor antenna efficiency quadratically constrained quadratic programming semidefinite relaxation constrained optimization

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On multiparametric/explicit NMPC for quadratically constrained Problems

On multiparametric/explicit NMPC for Quadratically Constrain...

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6th International-Federation-of-Automatic-Control (IFAC) Conference on Nonlinear-Model-Predictive-Control (NMPC)

作者： Diangelakis, Nikolaos A. Pappas, Iosif S. Pistikopoulos, Efstratios N. Texas A&M Univ Artie McFerrin Dept Chem Engn College Stn TX 77845 USA Texas A&M Univ Texas A&M Energy Inst College Stn TX 77845 USA

We present the expansion of the Basic Sensitivity Theorem to a second order Taylor approach and the implications to explicit model predictive control of quadratically constrained systems. The expansion enables the derivation of an algorithm for the analytical solution of convex multiparametric quadratically constraint programming (mpQCQP) problems and explicit quadratically constrained NMPC problems. We derive the analytical parametric expressions of the control actions for a quadratically constrained MPC problem and its corresponding critical regions. We show the piecewise non-linear form of the solution and closed loop validation of the results. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Multiparametric programming quadratically constrained quadratic programming explicit MPC

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Robust Adaptive Beamforming Based on Interference Covariance Matrix Reconstruction and Mismatched Steering Vector Compensation 3

Robust Adaptive Beamforming Based on Interference Covariance...

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3rd Asia-Pacific Conference on Antennas and Propagation (APCAP)

作者： Yan, Lu Yang, Xiaopeng Xi, Wen Zhang, Zongao Sarkar, Tapan K. Beijing Inst Technol Sch Informat & Elect Beijing 100081 Peoples R China Syracuse Univ Dept Elect Engn & Comp Sci Syracuse NY 13244 USA

ISBN: (纸本)9781479943548

The performance of adaptive beamforming degrades in presence of signal model mismatches. In particular, when the desired signal is present in training snapshots, the adaptive beamforming is quite sensitive to desired signal steering vector mismatch. Therefore, a robust adaptive beamforming for actual system is proposed based on the reconstruction of interference covariance matrix and mismatched steering vector compensation. In the proposed method, the interference covariance matrix is firstly reconstructed by using Root-MUSIC method to estimate Direction-of-Arrival (DOA) of signals, where the desired signal component is removed from the training snapshots. Subsequently, the mismatched desired signal steering vector is compensated by solving a quadratically constrained quadratic programming problem. Simulation results show that the performance of proposed algorithm outperforms the existing robust adaptive beamforming, and the output signal-to-interference-plus-noise ratio (SINR) is close to optimal values. Therefore, the proposed algorithm could be significantly effective for actual system.

关键词： Adaptive beamforming reconstructed interference covariance Root-MUSIC quadratically constrained quadratic programming

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Identification of Network Topology via quadratic Optimization

Identification of Network Topology via Quadratic Optimizatio...

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American Control Conference

作者： Sun, Chuangchuang Dai, Ran Iowa State Univ Dept Aerosp Engn Ames IA USA

ISBN: (纸本)9781479986842

Identification of network topology is to estimate the topology of a controllable and observable network with given number of nodes such that the identified network will satisfy the response between specified input and observed output. This paper examines the network topology identification (NTI) problems to find the original graph Laplacian from input-output data. A 'similar' set of state-space matrices satisfying the input-output response is firstly constructed through system identification procedure. Based on the similarity relationship, we reformulate the NTI problems as general quadratically constrained quadratic programming (QCQP) problems. The QCQP problem is then transformed into semidefinite programming (SDP) problem with a rank one constraint. An iterative rank minimization method is proposed to gradually approach the optimal solution. Examples are presented to verify the convergence of the proposed method.

关键词： Network Identification quadratically constrained quadratic programming Semidefinite programming Nonconvex Optimization

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constrained Primal-Dual Dynamics for QCQP with Applications to Economic Dispatch

Constrained Primal-Dual Dynamics for QCQP with Applications ...

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Control Conference Africa (CCA)

作者： Kim, Munyong Adegbege, Ambrose A. Coll New Jersey Elect & Comp Engn Dept Ewing NJ 08618 USA

We develop concise primal-dual dynamics for a class of quadratically constrained quadratic programming problems in power system optimization. Using a constrained Lagrangian reformulation of the problem and the classical stability result of Lyapunov, we establish the asymptotic convergence of the primal-dual dynamics. We demonstrate the efficiency of the proposed method on an economic power dispatch problem with transmission losses and we suggest a neural network architecture for real-time optimization. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Economic Dispatch Primal-Dual Dynamics constrained Optimization quadratically constrained quadratic programming

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Robust Formation Predictive Control of Image-based Mobile Robots With Neural Network Optimization 43

Robust Formation Predictive Control of Image-based Mobile Ro...

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43rd Chinese Control Conference (CCC)

作者： Zhu, Chengyu Wang, Yicheng Chen, HanTuo Liu, Andong Ni, Hongjie Zhejiang Univ Technol Coll Informat Engn Zhejiang Prov United Key Lab Embedded Syst Hangzhou 310023 Peoples R China Zhejiang Univ Technol Huzhou 313000 Peoples R China Huzhou Inst Digital Econ & Technol Huzhou 313000 Peoples R China

ISBN: (纸本)9798350366907;9789887581581

Vision-based control of mobile robots in formation has received a lot of attention. Real-time and efficient control is crucial for practical applications. An efficient model predictive control method is proposed using a recurrent neural network (RNN)-based optimizer to obtain optimal solutions in real-time. First, an efficient and robust model predictive control method is introduced for vision-based mobile robot formation control with stability constraints. Second, an RNN solver that decomposes the QCQP problem into a series of subproblems for solving is proposed. Finally, the applicability and performance of the proposed control scheme are demonstrated by typical hardware experiments.

关键词： Vision-based control formation control of mobile robots recurrent neural network quadratically constrained quadratic programming

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