Optimization of filament antennas using the Gauss-Newton method

The project of the Yagi-Uda antenna was optimized using the Gauss-Newton method. The optimization consisted of specifying value interval for directivity, front-to-back ratio and beamwidth and, starting from a pre-defined initial model, the best values for the length and spacing of the elements were determined. For the direct modeling, the method of moments on the integral Pocklington equation was used, which consisted of obtaining the values of directivity, front-to-back ratio and beamwidth from the length and spacing between known elements. The procedure was applied to the synthesis of Yagi-Uda antennas with five and six elements and the results were found to be as good as those obtained in the literature using other optimization methods.

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Global optimization with model-space preconditioning: Application to AVO inversion

Geophysics ◽

10.1190/1.2958008 ◽

2008 ◽

Vol 73 (5) ◽

pp. R71-R82 ◽

Cited By ~ 45

Author(s):

Somanath Misra ◽

Mauricio D. Sacchi

Keyword(s):

Global Optimization ◽

Local Minimum ◽

Optimization Problems ◽

A Priori ◽

Model Space ◽

Optimization Methods ◽

Search Space ◽

Initial Model ◽

Edge Preserving ◽

Nonlinear Operators

Linearized-inversion methods often have the disadvantage of dependence on the initial model. When the initial model is far from the global minimum, optimization is likely to converge to a local minimum. Optimization problems involving nonlinear relationships between data and model are likely to have more than one local minimum. Such problems are solved effectively by using global-optimization methods, which are exhaustive search techniques and hence are computationally expensive. As model dimensionality increases, the search space becomes large, making the algorithm very slow in convergence. We propose a new approach to the global-optimization scheme that incorporates a priori knowledge in the algorithm by preconditioning the model space using edge-preserving smoothing operators. Such nonlinear operators acting on the model space favorably precondition or bias the model space for blocky solutions. This approach not only speeds convergence but also retrieves blocky solutions. We apply the algorithm to estimate the layer parameters from the amplitude-variation-with-offset data. The results indicate that global optimization with model-space-preconditioning operators provides faster convergence and yields a more accurate blocky-model solution that is consistent with a priori information.

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AN APPROXIMATE ANALYTICAL EXPRESSION FOR RESISTANCE OF THE VERTICAL GROUNDING ELECTRODE PLACED IN MULTILAYERED MEDIA

10.7562/se2018.8.01.08 ◽

2018 ◽

Vol 8 (1) ◽

Author(s):

DEJAN JOVANOVIĆ ◽

NENAD CVETKOVIĆ ◽

MIODRAG STOJANOVIĆ ◽

MARINKO BARUKČIĆ ◽

ŽELJKO HEDERIĆ ◽

...

Keyword(s):

Method Of Moments ◽

Specific Conductivity ◽

Optimization Procedure ◽

Optimization Methods ◽

Data Sets ◽

Multilayered Media ◽

Approximate Analytical Expression ◽

Vertical Electrode ◽

Grounding Electrode

An expression for the resistance of the grounding electrode placed in the in homogeneous ground approximated by a finite number of homogeneous layers of constant specific conductivity has been evaluated and proposed in the paper. The expression is obtained by optimization procedure, based on processing of data sets obtained as a result of the analysis which includes using of the Green’s function for the point source in multilayered soil and the Method of Moments. The approach has been applied to the characterization of a vertical electrode placed in the three-layered soil. Key words: Green’s functions methods, Grounding, Optimization methods.

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SPAN: A Stochastic Projected Approximate Newton Method

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v34i02.5511 ◽

2020 ◽

Vol 34 (02) ◽

pp. 1520-1527

Author(s):

Xunpeng Huang ◽

Xianfeng Liang ◽

Zhengyang Liu ◽

Lei Li ◽

Yue Yu ◽

...

Keyword(s):

Theoretical Analysis ◽

Convergence Rate ◽

Newton Method ◽

Hessian Matrix ◽

Approximation Error ◽

Optimization Methods ◽

Second Order ◽

Low Rank ◽

Low Rank Approximation ◽

Benchmark Datasets

Second-order optimization methods have desirable convergence properties. However, the exact Newton method requires expensive computation for the Hessian and its inverse. In this paper, we propose SPAN, a novel approximate and fast Newton method. SPAN computes the inverse of the Hessian matrix via low-rank approximation and stochastic Hessian-vector products. Our experiments on multiple benchmark datasets demonstrate that SPAN outperforms existing first-order and second-order optimization methods in terms of the convergence wall-clock time. Furthermore, we provide a theoretical analysis of the per-iteration complexity, the approximation error, and the convergence rate. Both the theoretical analysis and experimental results show that our proposed method achieves a better trade-off between the convergence rate and the per-iteration efficiency.

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