Constrained Best Euclidean Distance Embedding on a Sphere: A Matrix Optimization Approach

Each pixel in the hyperspectral unmixing process is modeled as a linear combination of endmembers, which can be expressed in the form of linear combinations of a number of pure spectral signatures that are known in advance. However, the limitation of Gaussian random variables on its computational complexity or sparsity affects the efficiency and accuracy. This paper proposes a novel approach for the optimization of measurement matrix in compressive sensing (CS) theory for hyperspectral unmixing. Firstly, a new Toeplitz-structured chaotic measurement matrix (TSCMM) is formed by pseudo-random chaotic elements, which can be implemented by a simple hardware; secondly, rank revealing QR factorization with eigenvalue decomposition is presented to speed up the measurement time; finally, orthogonal gradient descent method for measurement matrix optimization is used to achieve optimal incoherence. Experimental results demonstrate that the proposed approach can lead to better CS reconstruction performance with low extra computational cost in hyperspectral unmixing.

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An Inexact Smoothing Newton Method for Euclidean Distance Matrix Optimization Under Ordinal Constraints

Journal of Computational Mathematics ◽

10.4208/jcm.1702-m2016-0748 ◽

2017 ◽

Vol 35 (4) ◽

pp. 469-485 ◽

Cited By ~ 2

Author(s):

Qingna Li and Houduo Qi

Keyword(s):

Newton Method ◽

Euclidean Distance ◽

Distance Matrix ◽

Smoothing Newton Method ◽

Euclidean Distance Matrix ◽

Matrix Optimization

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Euclidean Distance Matrix Optimization for Sensor Network Localization *

Cooperative Localization and Navigation ◽

10.1201/9780429507229-5 ◽

2019 ◽

pp. 99-126 ◽

Cited By ~ 1

Author(s):

Jörg Fliege ◽

Hou-Duo Qi ◽

Naihua Xiu

Keyword(s):

Sensor Network ◽

Euclidean Distance ◽

Distance Matrix ◽

Euclidean Distance Matrix ◽

Sensor Network Localization ◽

Matrix Optimization ◽

Network Localization

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Feasibility and a fast algorithm for Euclidean distance matrix optimization with ordinal constraints

Computational Optimization and Applications ◽

10.1007/s10589-020-00189-9 ◽

2020 ◽

Vol 76 (2) ◽

pp. 535-569

Author(s):

Si-Tong Lu ◽

Miao Zhang ◽

Qing-Na Li

Keyword(s):

Fast Algorithm ◽

Euclidean Distance ◽

Distance Matrix ◽

Euclidean Distance Matrix ◽

Matrix Optimization

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Multi-user hybrid precoding for mmWave massive MIMO systems with sub-connected structure

EURASIP Journal on Wireless Communications and Networking ◽

10.1186/s13638-021-02031-0 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Jianhe Du ◽

Zekun Wang ◽

Yang Zhang ◽

Yalin Guan ◽

Libiao Jin

Keyword(s):

Interference Cancellation ◽

Optimization Problems ◽

Mimo Systems ◽

Optimization Approach ◽

Hardware Complexity ◽

Matrix Optimization ◽

Hybrid Precoding ◽

Connected Structure ◽

Sum Rate ◽

Simulation Results

AbstractHybrid precoding achieves a compromise between the sum rate and hardware complexity of millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems. However, most prior works on multi-user hybrid precoding only consider the full-connected structure. In this paper, a novel multi-user hybrid precoding algorithm is proposed for the sub-connected structure. Based on the improved successive interference cancellation (SIC), the analog precoding matrix optimization problem is decomposed into multiple analog precoding sub-matrix optimization problems. Further, a near-optimal analog precoder is designed through factorizing the precoding sub-matrix for each sub-array. Furthermore, digital precoding is designed according to the block diagonalization (BD) technology. Finally, the water-filling power allocation method is used to further improve the communication quality. The extensive simulation results demonstrate that the sum rate of the proposed algorithm is higher than the existing hybrid precoding methods with the sub-connected structure, and has higher energy efficiency compared with existing approaches. Moreover, the proposed algorithm is closer to the state-of-the-art optimization approach with the full-connected structure. In addition, the simulation results also verify the effectiveness of the proposed hybrid precoding design of the uniform planar array (UPA).

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Interactive multiobjective DEA target setting using lexicographic DDF

RAIRO - Operations Research ◽

10.1051/ro/2019105 ◽

2020 ◽

Vol 54 (6) ◽

pp. 1703-1722 ◽

Cited By ~ 1

Author(s):

Narges Soltani ◽

Sebastián Lozano

Keyword(s):

Efficient Frontier ◽

Directional Distance Function ◽

Fixed Number ◽

Optimization Approach ◽

Target Setting ◽

Interactive Process ◽

Decision Making Unit ◽

Setting Approach ◽

Promising Area ◽

Current Region

In this paper, a new interactive multiobjective target setting approach based on lexicographic directional distance function (DDF) method is proposed. Lexicographic DDF computes efficient targets along a specified directional vector. The interactive multiobjective optimization approach consists in several iteration cycles in each of which the Decision Making Unit (DMU) is presented a fixed number of efficient targets computed corresponding to different directional vectors. If the DMU finds one of them promising, the directional vectors tried in the next iteration are generated close to the promising one, thus focusing the exploration of the efficient frontier on the promising area. In any iteration the DMU may choose to finish the exploration of the current region and restart the process to probe a new region. The interactive process ends when the DMU finds its most preferred solution (MPS).

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