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检索条件"主题词=Semidefinite Programming"

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Solution of the Propeller Conjecture in R~3 12

Solution of the Propeller Conjecture in R~3

引用

ACM Symposium on Theory of Computing

作者： Steven Heilman Aukosh Jagannath Assaf Naor Courant Institute NYU New York NY USA

ISBN: (纸本)9781450312455

It is shown that every measurable partition {A_1,...,A_k} of R~3 satisfies ∑_(i=1)~k ‖∫_(A_i) xe~(-1/2‖x‖_2~2)dx‖_2~2 ≤ 9π~2. (1) Let {P_1, P_2, P_3} be the partition of R~2 into 120° sectors centered at the origin. The bound (1) is sharp, with equality holding if A_i = P_i × R for i ∈ {1, 2, 3} and A_i = 0 for i ∈ {4,...,k}. This settles positively the 3-dimensional Propeller Conjecture of Khot and Naor (FOCS 2008). The proof of (1) reduces the problem to a finite set of numerical inequalities which are then verified with full rigor in a computer-assisted fashion. The main consequence (and motivation) of (1) is complexity-theoretic: the Unique Games hardness threshold of the Kernel Clustering problem with 4×4 centered and spherical hypothesis matrix equals 2π/3.

关键词： Theory Kernel clustering Unique games hardness semidefinite programming Grothendieck inequalities

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Sum of Squares Approaches for Control of Continuous-Time Recurrent Fuzzy Systems

Sum of Squares Approaches for Control of Continuous-Time Rec...

引用

Mediterranean Conference on Control & Automation

作者： Stefan Gering Andreas Schwung Thomas Gussner Jurgen Adamy Technische Universitat Darmstadt Control Theory & Robotics Lab

ISBN: (纸本)9781479909964

In recent years, a concise theory of recurrent fuzzy systems has emerged and methods for utilizing these fuzzy systems with dynamics for modeling and fault detection were developed. At the same time, sum of squares decompositions in conjunction with semidefinite programming were successfully applied for the synthesis of controllers for polynomial systems. In this paper, we combine both approaches and present sum of squares based control strategies for continuous-time recurrent fuzzy systems. The system dynamics under consideration is defined by gradients at discrete points in the input-state space. An alternative description as piecewise polynomial system is possible. This motivates to utilize a controller switching between local polynomial control laws. We propose three different approaches for controller synthesis based on this idea and demonstrate this new synthesis method by means of an example. In addition, advantages and drawbacks of the approaches are discussed.

关键词： Continuous-Time Recurrent Fuzzy Systems Sum of Squares Controller Synthesis Switched Controller Polynomial Systems semidefinite programming

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Robust Quadratic Optimal Control of Linear Systems with Ellipsoid-Set Learning

Robust Quadratic Optimal Control of Linear Systems with Elli...

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European Control Conference (ECC)

作者： Xuehui Mal Yutong Chen Shiliang Zhang Yushuai Li Fucai Qian Zhiyong Sun School of Automation and Information Engineering Xi'an University of Technology Xi'an China Department of Electronic Engineering Tsinghua University Beijing China Department of Informatics University of Oslo Oslo Norway Department of Computer Science Aalborg University Aalborg Denmark Department of Electrical Engineering Eind-hoven University of Technology Netherlands

ISBN: (数字)9783907144107

ISBN: (纸本)9798331540920

Despite the celebrated success of linear quadratic Gaussian control (LQG) for stochastic systems, LQG approaches are inefficient in handling systems with non-Gaussian noises. This paper is concerned with linear quadratic control of discrete-time systems with bounded noises and unobservable system states. We describe such noises and system states by ellipsoidal sets, enabling the establishment of boundaries for those uncertainties in the control. Further, we learn and update the ellipsoidal sets for the system states by an ellipsoidal set-membership filter. With the learned ellipsoidal sets, we derive a robust state-feedback optimal control law by solving a rendered semidefinite programming problem. Simulation results demonstrate the enhanced control performance by the proposed method.

关键词： Robust control Linear systems Discrete-time systems semidefinite programming Uncertainty Stochastic systems Simulation

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Hybrid Robust Beamforming against DoA Estimation Mismatch and Moving Interference

Hybrid Robust Beamforming against DoA Estimation Mismatch an...

引用

IEEE International Conference on Communications in China (ICCC)

作者： Yu Du Minjian Zhao College of Information Science and Electronic Engineering Zhejiang University Hangzhou China

ISBN: (数字)9798350378412

ISBN: (纸本)9798350378429

The direction of arrival (DoA) estimation mismatch and moving interference severely degrade the performance of beamforming. Null broadening techniques have been extensively studied to handle these issues. They block interference by generating broad nulls in the direction of interference. However, the conventional fully digital null broadening methods, which require one radio frequency (RF) chain per antenna, are not viable for large-scale antenna arrays due to the high cost and high power consumption. Moreover, they produce sharp main beams, which, despite concentrating energy, are more sensitive to DoA estimation mismatch. To overcome the challenges associated with hardware limitations and mismatches in DoA estimation, this paper investigates a partially connected hybrid beamforming (HBF) architecture. We propose an alternating fractional programming semidefinite relaxation (SDR) algorithm, which addresses the problem by dividing it into analog and digital beamforming matrices and transforming it into a semidefinite programming (SDP) problem. This approach achieves broad nulls in the interference region and flatten the main beam. Simulation results demonstrate that this method effectively combats DoA estimation mismatch and moving interference, outperforming traditional algorithms.

关键词： Radio frequency Direction-of-arrival estimation semidefinite programming Array signal processing Heuristic algorithms Simulation Estimation

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Robust Beamforming Design for MIMO-OFDM Joint Radar and Communication Systems

Robust Beamforming Design for MIMO-OFDM Joint Radar and Comm...

引用

IEEE International Conference on Communications (ICC)

作者： Chi-Han Chou Ming-Chun Lee Po-Chun Kang Ta-Sung Lee Institute of Communications Engineering National Yang Ming Chiao Tung University Hsinchu Taiwan

ISBN: (数字)9781728190549

ISBN: (纸本)9781728190556

The investigation of the joint radar and communication (RadCom) systems has drawn attention in recent years. However, the relevant investigation of the multiple-input multiple-output (MIMO)-orthogonal frequency division multiplexing (OFDM) based joint RadCom system is incomplete, especially for the robust beamforming design. To fill this gap, by first formulating a robust design problem that jointly considers the estimation of ranges, Doppler velocities, and angles of targets under uncertainty along with the system capacity, this paper studies the robust beamforming design for the MIMO-OFDM joint RadCom system. Then, since the design problem can be reformulated as a semidefinite programming with rank-1 constraint, we propose using the semidefinite relaxation to solve the problem. Simulation results show that our proposed design can outperform the reference methods in the literature.

关键词： Uncertainty semidefinite programming Array signal processing Simulation OFDM Estimation Radar

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Topology Optimization, Fabrication Adaptivity, and Model-Data Assimilation of Novel Photonic Materials

Topology Optimization, Fabrication Adaptivity, and Model-Dat...

引用

作者： Freund,Robert,Peraire,Jaime,Nguyen,Cuong, Massachusetts Institute of Technology Cambridge United States

Novel materials such as photonic crystals, nanoplasmonics, and metamaterials are engineered to interact with and control electromagnetic waves in ways that cannot be achieved with conventional materials. Such materials are very important in many optical devices including waveguides, fibers, lasers, optical lenses, cancer theranostics, biological and chemical sensing, energy harvesting, etc. Fundamental challenges abound about the design and fabrication of these materials. The issue of fabrication adaptivity adapting a computed design to actual fabrication is particularly important in practical applications. We have developed effective systematic numerical methods and tools for the optimal design of photonic materials with particular emphasis on novel applications which are of direct interest to the Air Force. We have worked on three research fronts 1 robust, efficient and accurate numerical methods for solving acoustic and electromagnetic wave equations in realistic geometries, 2 Gaussian functional regression methods for quantifying uncertainties in the mathematical models, and 3 efficient and robust accelerated first-order methods for solving large-scale PDE-constrained optimization problems arising from mathematical formulations of the design problem.

关键词： Materials Photonic crystals Energy harvesting Mathematical models Optical lenses Wave equations Fabrication Geometry Mathematics Metamaterials Optimization Theranostics Topology Uncertainty Wave propagation Periodic media Band-gap optimization semidefinite programming Photonic crystal design Phononic crystal design Conic optimization First-order methods Greedy methods Robust regularization

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CoMP in Heterogeneous Networks: Linear Transceiver Design Using the Minimum Weighted Arithmetic-MSE Criterion

CoMP in Heterogeneous Networks: Linear Transceiver Design Us...

引用

International OFDM Workshop

作者： Tarik Akbudak Andreas Czylwik Chair of Communication Systems University of Duisburg-Essen

ISBN: (纸本)9783800733606

Coordinated multipoint transmission (CoMP) is considered for a heterogeneous network (HetNet) where different kinds of base stations (BS) are located. We focus on linear transceiver design with the goal of maximizing the weighted sum-rate in the downlink of a multipleinput multiple-output orthogonal frequency division multiple access (MIMO-OFDMA) system, where each subchannel is allocated to a single user (termed as single-user MIMOOFDMA). We address this in the context of minimizing the weighted arithmetic mean of the mean-square-errors (MSEs), i.e., weighted arithmetic-MSE minimization. The problem is shown to be non-convex for a given rank constraint on the number of streams at a subchannel. Therefore, the solutions to the rank-constrained problem are suboptimal in general. We show that iterative approaches provide more efficient suboptimal solutions compared to the rank-relaxed approach, especially in a heterogeneous network where highly imbalanced base stations are located.

关键词： Weighted sum-rate maximization Linear transceiver design Second-order cone programming semidefinite programming

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Planted clique detection below the noise floor using low-rank sparse PCA

Planted clique detection below the noise floor using low-ran...

引用

IEEE International Conference on Acoustics, Speech and Signal Processing

作者： A. B. Cook B. A. Miller Dept. of Appl. Math. Brown Univ. Providence RI USA

ISBN: (纸本)9781467369985

Detection of clusters and communities in graphs is useful in a wide range of applications. In this paper we investigate the problem of detecting a clique embedded in a random graph. Recent results have demonstrated a sharp detectability threshold for a simple algorithm based on principal component analysis (PCA). Sparse PCA of the graph's modularity matrix can successfully discover clique locations where PCA-based detection methods fail. In this paper, we demonstrate that applying sparse PCA to low-rank approximations of the modularity matrix is a viable solution to the planted clique problem that enables detection of small planted cliques in graphs where running the standard semidefinite program for sparse PCA is not possible.

关键词： community detection graph analysis planted clique detection semidefinite programming sparse principal component analysis principal components analysis Passive Cutaneous Anaphylaxis Modularity Decks inspection methods

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Spatial Array Thinning for Interference Cancellation Under Connectivity Constraints

Spatial Array Thinning for Interference Cancellation Under C...

引用

IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Hamed Nosrati Elias Aboutanios David B. Smith School of Electrical Engineering and Telecommunication University of New South Wales Australia Data61 CSIRO Australia

ISBN: (纸本)9781538646595

Array spatial thinning is employed to select the most effective antenna elements in a large phased array for optimum performance concerning hardware and computational costs, in conjunction with managing element failure and radio interference mitigation. We formulate spatial array thinning under connectivity constraints to make the thinning applicable in large arrays. By introducing graph optimization, the problem is recast as a k-clique version of a generalized minimum clique problem. Furthermore, by studying optimum clustering for the proposed formulation, we show by an example that the unconstrained thinning performance is achievable, even with connectivity constraints.

关键词： Array thinning antenna selection beam-forming semidefinite programming convex optimization graph optimization generalized minimum clique problem Beamforming Thinning THINNING CANCELLATIONS Convex function singling arrays antenna element optimum performance Constraint

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Local Lipschitz Constant Computation of ReLU-FNNs: Upper Bound Computation with Exactness Verification

Local Lipschitz Constant Computation of ReLU-FNNs: Upper Bou...

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European Control Conference (ECC)

作者： Yoshio Ebihara Xin Dai Tsuyoshi Yuno Victor Magron Dimitri Peaucelle Sophie Tarbouriech Graduate School of Information Science and Electrical Engineering Kyushu University Fukuoka Japan LAAS-CNRS Universite de Toulouse CNRS Toulouse France

ISBN: (数字)9783907144107

ISBN: (纸本)9798331540920

This paper is concerned with the computation of the local Lipschitz constant of feedforward neural networks (FNNs) with activation functions being rectified linear units (ReLUs). The local Lipschitz constant of an FNN for a target input is a reasonable measure for its quantitative evaluation of the reliability. By following a standard procedure using multipliers that capture the behavior of ReLU s, we first reduce the upper bound computation problem of the local Lipschitz constant into a semidefinite programming problem (SDP). Here we newly introduce copositive multipliers to capture the ReLU behavior accurately. Then, by considering the dual of the SDP for the upper bound computation, we second derive a viable test to conclude the exactness of the computed upper bound. However, these SDPs are intractable for practical FNNs with hundreds of ReLUs. To address this issue, we further propose a method to construct a reduced order model whose input-output property is identical to the original FNN over a neighborhood of the target input. We finally illustrate the effectiveness of the model reduction and exactness verification methods with numerical examples of practical FNNs.

关键词： Fuzzy control Upper bound semidefinite programming Europe Reduced order systems Feedforward neural networks Reliability

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