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22nd IEEE Signal Processing and Communications Applications Conference (SIU)

作者： Dedeoglu, Mehmet Alp, Yasar Kemal Arikan, Orhan Ihsan Dogramaci Bilkent Univ Elekt Elekt Muhendisligi Bolumu Ankara Turkey ASELSAN AS Radar Elekt Harp & Istihbarat Sistemleri Grubu Ankara Turkey

ISBN: (纸本)9781479948741

Finite impulse response (FIR) filters have been a primary topic of digital signal processing since their inception. Although FIR filter design is an old problem, with the developments of fast convex solvers, convex modelling approach for FIR filter design has become an active research topic. In this work, we propose a new method based on convex programming for designing FIR filters with the desired frequency characteristics. FIR filter design problem, which is modelled as a non-convex quadratically constrained quadratic program (QCQP), is transformed to a semidefinite program (SDP). By relaxing the constraints, a convex programming problem, which we call RSDP(Relaxed Semidefinite Program), is obtained. Due to the relaxation, solution to the RSDPs fails to be rank-1. Typically used rank-1 approximations to the obtained RSDP solution does not satisfy the constraints. To overcome this issue, an iterative algorithm is proposed, which provides a sequence of solutions that converge to a rank-1 matrix. Conducted experiments and comparisons demonstrate that proposed method successfully designs FIR filters with highly flexible frequency characteristics.

关键词： Semidefinite programming FIR filter quadratically constrained quadratic programming rank refinement

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Null Broadening Adaptive Beamforming Based on Semidefinite programming 13

Null Broadening Adaptive Beamforming Based on Semidefinite P...

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13th IEEE International Conference on Signal Processing (ICSP)

作者： Qian, Junhui He, Zishu Zhang, Yile Wu, Bo Univ Elect Sci & Technol China Dept EE Chengdu 611731 Sichuan Peoples R China Georgia Inst Technol Atlanta GA 30332 USA

ISBN: (纸本)9781509013456

In this paper, we introduce a procedure for the null broadening algorithm design with respect to the perturbation of the interference location. This method is based on maximizing the array output signal-to-interference-plus-noise-ratio (SINR) subject to quadratic constraints. The design problem can be cast as a fractional quadratically constrained quadratic programming (QCQP) problem that can be solved efficiently using the semidefinite programming (SDP) techniques, the semidefinite relaxation can be used to obtain a lower bound on the optimal objective function. This proposed approach imposes broadened nulls towards the interference region while possesses well-maintained pattern. Theoretical analysis and numerical results demonstrate that the performance of proposed adaptive beamformer is almost always close to optimal.

关键词： Robust adaptive beamforming beampattern shaping constraints quadratically constrained quadratic programming semidefinite programming

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A Decomposition Method for Nonconvex quadratically constrained quadratic Programs

A Decomposition Method for Nonconvex Quadratically Constrain...

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American Control Conference (ACC)

作者： Sun, Chuangchuang Dai, Ran Iowa State Univ Aerosp Engn Dept Ames IA 50011 USA

ISBN: (纸本)9781509059928

This paper examines the nonconvex quadratically constrained quadratic programming (QCQP) problems using a decomposition method. It is well known that a QCQP can be transformed into a rank-one constrained optimization problem. Finding a rank-one matrix is computationally complicated, especially for large scale QCQPs. A decomposition method is applied to decompose the single rank-one constraint on original unknown matrix into multiple rank-one constraints on small scale submatrices. An iterative rank minimization (IRM) algorithm is then proposed to gradually approach all of the rank-one constraints. To satisfy each rank-one constraint in the decomposed formulation, linear matrix inequalities (LMIs) are introduced in IRM with local convergence analysis. The decomposition method reduces the overall computational cost by decreasing size of LMIs, especially when the problem is sparse. Simulation examples with comparative results obtained from an alternative method are presented to demonstrate advantages of the proposed method.

关键词： quadratically constrained quadratic programming Rank Constraint Optimization Semidefinite programming Matrix Decomposition Sparse Matrix

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Real-time Relative Pose Estimation for Muti-UAV Systems Using Odometry and UWB Measurements 43

Real-time Relative Pose Estimation for Muti-UAV Systems Usin...

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43rd Chinese Control Conference (CCC)

作者： Qiao, Xian Yu, Chengpu Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China Beijing Inst Technol Chongqing Innovat Ctr Chongqing 401147 Peoples R China

ISBN: (纸本)9798350366907;9789887581581

This article studies the problem of real-time relative pose estimation of multi-UAV systems based on inter-UAV distance measurement and onboard odometry. In large-scale UAV systems, the centralized localization problem using only distance measurements is challenging from the perspective of computational burden. The concerned relative pose estimation problem is formulated as a squared distance weighted least squares problem and is then decomposed to be executed on each UAV. Constraints on the relative poses of neighboring UAVs with mutual distance measurements are added to the problem under the condition that some UAVs lack direct distance measurements, subsequently transforming it into a quadratically constrained quadratic programming (QCQP) form for solving. Simulation experiments show that the proposed optimization problem is effective in real-time relative pose estimation of large-scale UAVs with distance measurements and odometry, and can yield more accurate pose estimates than the relevant literature.

关键词： multi-UAV systems relative pose estimation quadratically constrained quadratic programming sensor fusion

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Rapid Initialization Method of Unmanned Aerial Vehicle Swarm Based on VIO-UWB in Satellite Denial Environment

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DRONES 2024年第7期8卷 339-339页

作者： Wang, Runmin Deng, Zhongliang Beijing Univ Post & Telecommun Sch Elect Engn 10 Xitucheng RdNorth Taipingzhuang Beijing 100876 Peoples R China

In environments where satellite signals are blocked, initializing UAV swarms quickly is a technical challenge, especially indoors or in areas with weak satellite signals, making it difficult to establish the relative position of the swarm. Two common methods for initialization are using the camera for joint SLAM initialization, which increases communication burden due to image feature point analysis, and obtaining a rough positional relationship using prior information through a device such as a magnetic compass, which lacks accuracy. In recent years, visual-inertial odometry (VIO) technology has significantly progressed, providing new solutions. With improved computing power and enhanced VIO accuracy, it is now possible to establish the relative position relationship through the movement of drones. This paper proposes a two-stage robust initialization method for swarms of more than four UAVs, suitable for larger-scale satellite denial scenarios. Firstly, the paper analyzes the Cram & eacute;r-Rao lower bound (CRLB) problem and the moving configuration problem of the cluster to determine the optimal anchor node for the algorithm. Subsequently, a strategy is used to screen anchor nodes that are close to the lower bound of CRLB, and an optimization problem is constructed to solve the position relationship between anchor nodes through the relative motion and ranging relationship between UAVs. This optimization problem includes quadratic constraints as well as linear constraints and is a quadratically constrained quadratic programming problem (QCQP) with high robustness and high precision. After addressing the anchor node problem, this paper simplifies and improves a fast swarm cooperative positioning algorithm, which is faster than the traditional multidimensional scaling (MDS) algorithm. The results of theoretical simulations and actual UAV tests demonstrate that the proposed algorithm is advanced, superior, and effectively solves the UAV swarm initialization problem

关键词： cooperative positioning quadratically constrained quadratic programming multidimensional scaling (MDS) Cram & eacute r-Rao lower bound (CRLB) GNSS-denied

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Null broadening adaptive beamforming based on covariance matrix reconstruction and similarity constraint

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EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING 2017年第1期2017卷 1页

作者： Qian, Junhui He, Zishu Xie, Julan Zhang, Yile Univ Elect Sci & Technol China Sch Elect Engn 2006 Xi Yuan Ave Chengdu Peoples R China

In this paper, a procedure for the null broadening algorithm design with respect to the nonstationary interference is proposed. In contrast to previous works, we first impose nulls toward the regions of the nonstationary interference based on the reconstruction of the interference-plus-noise covariance matrix. Additionally, in order to provide a restriction on the shape of the beam pattern, a similarity constraint is enforced at the design stage. Then, the adaptive weight vector can be computed via maximizing a new signal-to-interference-plus-noise ratio (SINR) criterion subject to similarity constraint. Mathematically, the design original problem is expressed as a nonconvex fractional quadratically constrained quadratic programming (QCQP) problem with additional constraint, which can be converted into a convex optimisation problem by semidefinite programming (SDP) techniques. Finally, an optimal solution can be found by using the Charnes-Cooper transformation and the rank-one matrix decomposition theorem. Several numerical examples are performed to validate the performance of the proposed algorithm.

关键词： Robust adaptive beamforming Similarity constraint quadratically constrained quadratic programming Semidefinite programming

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quadratic problems with two quadratic constraints: convex quadratic relaxation and strong lagrangian duality

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RAIRO-OPERATIONS RESEARCH 2021年第1-Sup期55卷 S2905-S2922页

作者： Hamdi, Abdelouahed Taati, Akram Almaadeed, Temadher A. Qatar Univ Dept Math Stat & Phys Doha Qatar Univ Guilan Fac Math Sci Rasht Iran

In this paper, we study a nonconvex quadratic minimization problem with two quadratic constraints, one of which being convex. We introduce two convex quadratic relaxations (CQRs) and discuss cases, where the problem is equivalent to exactly one of the CQRs. Particularly, we show that the global optimal solution can be recovered from an optimal solution of the CQRs. Through this equivalence, we introduce new conditions under which the problem enjoys strong Lagrangian duality, generalizing the recent condition in the literature. Finally, under the new conditions, we present necessary and sufficient conditions for global optimality of the problem.

关键词： quadratically constrained quadratic programming convex quadratic relaxation strong duality SDO-relaxation

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A QCQP-based splitting SQP algorithm for two-block nonconvex constrained optimization problems with application

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2021年 390卷 113368-113368页

作者： Jian, Jinbao Liu, Pengjie Yin, Jianghua Zhang, Chen Chao, Miantao Guangxi Univ Nationalities Guangxi Key Lab Hybrid Computat & IC Design Anal Coll Math & Phys Ctr Appl Math & Artificial Intelligence Nanning 530006 Peoples R China Guangxi Univ Coll Math & Informat Sci Nanning 530004 Peoples R China Guangxi Sci & Technol Normal Univ Coll Math & Comp Sci Laibin 546199 Peoples R China Univ Shanghai Sci & Technol Sch Mech Engn Shanghai 200093 Peoples R China

This paper discusses a class of two-block nonconvex smooth optimization problems with nonlinear constraints. Based on a quadratically constrained quadratic programming (QCQP) approximation, an augmented Lagrangian function (ALF), and a Lagrangian splitting technique into small-scale subproblems, we propose a novel sequential quadratic programming (SQP) algorithm. First, inspired by the augmented Lagrangian method (ALM), we penalize the quadratic equality constraints associated with the QCQP approximation subproblem in its objective by means of the ALF, and then split the resulting subproblem into two small-scale ones, but both of them are not quadratic programming (QP) due to the square of the quadratic equality constraints in the objective. Second, by ignoring the three-order infinitesimal arising from the squared term, the two small-scale subproblems are reduced to two standard QP subproblems, which can yield an improved search direction. Third, taking the ALF of the discussed problem as a merit function, the next iterate point is generated by the Armijo line search. As a result, a new SQP method, called QCQP-based splitting SQP method, is proposed. Under suitable conditions, the global convergence, strong convergence, iteration complexity and convergence rate of the proposed method are analyzed and obtained. Finally, preliminary numerical experiments and applications were carried out, and these show that the proposed method is promising. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Two-block nonconvex constrained optimization quadratically constrained quadratic programming Sequential quadratic programming Splitting method Convergence analysis

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Exactness Conditions for Semidefinite programming Relaxations of Generalization of the Extended Trust Region Subproblem

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MATHEMATICS OF OPERATIONS RESEARCH 2023年第3期48卷 1235-1253页

作者： Jiang, Rujun Li, Duan Fudan Univ Sch Data Sci Shanghai 200433 Peoples R China City Univ Hong Kong Sch Data Sci Hong Kong Peoples R China

The extended trust region subproblem (ETRS) of minimizing a quadratic objective over the unit ball with additional linear constraints has attracted a lot of attention in the last few years because of its theoretical significance and wide spectra of applications. Several sufficient conditions to guarantee the exactness of its semidefinite programming (SDP) relaxation have been recently developed in the literature. In this paper, we consider a generalization of the extended trust region subproblem (GETRS), in which the unit ball constraint in the ETRS is replaced by a general, possibly nonconvex, quadratic constraint, and the linear constraints are replaced by a conic linear constraint. We derive sufficient conditions for guaranteeing the exactness of the SDI' relaxation of the GETRS under mild assumptions. Our main tools are two clacses of convex relaxations for the GETRS based on either a simultaneous diagonalization transformation of the quadratic forms or linear combinations of the quadratic forms. We also compare our results to the existing sufficient conditions in the literature. Finally, we extend our results to derive a new sufficient condition for the exactness of the SDP relaxation of general diagonal quadratically constrained quadratic programs, where each quadratic function is associated with a diagonal matrix.

关键词： quadratically constrained quadratic programming extended trust region subproblem semidefinite programming second order cone programming

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A per-node granularity decentralized optimal power flow for radial distribution networks with PV and EV integration

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2020年 116卷 105513-000页

作者： Tang, Chong Liu, Mingbo Liu, Qingkai Dong, Ping South China Univ Technol Sch Elect Power Engn Guangzhou 510640 Guangdong Peoples R China

With the large scale of distributed energy resources integrated into distribution systems, the development of effective power management for controllable components is becoming an increasingly important concern. This paper focuses on solving the optimal power flow problem in a distribution network with a fully decentralized mode that has massive photovoltaics and electric vehicles. First, an optimal power flow model considering photovoltaics and electric vehicles as controllable agents was established to achieve low network loss, low curtailment of photovoltaic resources, and high satisfaction of electric vehicle owners. Second, a novel linearized power flow model was proposed to produce per-node granularity communication. Thus, each node only needed to exchange the voltage message with its neighboring nodes. Then a decentralized quadratically constrained quadratic programming model based on the alternating direction method of multipliers was built to solve the optimal power flow problem. Next, a closed-form iterative solution method for the decentralized optimization was developed to improve the calculation speed for each iteration. Finally, case studies for a real 35-bus distribution system and a real 110-bus distribution system in China were used to verify the effectiveness of the proposed method.

关键词： Distribution network Photovoltaic Electric vehicle Optimal power flow Per-node granularity quadratically constrained quadratic programming

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