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Spatial interpolation using nonlinear mathematical programming models for estimation of missing precipitation records

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HYDROLOGICAL SCIENCES JOURNAL 2012年第3期57卷 383-406页

作者： Teegavarapu, Ramesh S. V. Florida Atlantic Univ Dept Civil Engn Boca Raton FL 33431 USA

New mathematical programming models are proposed, developed and evaluated in this study for estimating missing precipitation data. These models use nonlinear and mixed integer nonlinear mathematical programming (MINLP) formulations with binary variables. They overcome the limitations associated with spatial interpolation methods relevant to the arbitrary selection of weighting parameters, the number of control points within a neighbourhood, and the size of the neighbourhood itself. The formulations are solved using genetic algorithms. Daily precipitation data obtained from 15 rain gauging stations in a temperate climatic region are used to test and derive conclusions about the efficacy of these methods. The developed methods are compared with some nave approaches, multiple linear regression, nonlinear least-square optimization, kriging, and global and local trend surface and thin-plate spline models. The results suggest that the proposed new mathematical programming formulations are superior to those obtained from all the other spatial interpolation methods tested in this study.

关键词： missing precipitation data spatial interpolation genetic algorithms nonlinear optimization methods mixed integer mathematical programming (MINLP) multiple linear regression nonlinear least squares approach thin-plate splines trend surface models Kentucky USA

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Novel approach to measurement-based load modeling via analog and Jacobi-based methods

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2013年第Dec.期53卷 329-337页

作者： Deese, Anthony Nwankpa, C. O. Coll New Jersey Dept Elect & Comp Engn Ewing NJ 08628 USA Drexel Univ Dept Elect & Comp Engn Philadelphia PA 19104 USA

This paper addresses a concrete problem in the field of power engineering. Although measurement-based modeling techniques have potential to drastically improve the quality of load representation in power system studies and positively affect results, they are not applied (in industry) for reasons of computational complexity. These limitations stem from the optimization methods (e.g. Newton-Raphson) and hardware implementations (e.g. digital computer) generally employed. In this work, the authors examine a simple, alternative method which relies on Jacobi optimization and analog emulation hardware to reduce computational complexity, facilitate online applications, and make measurement-based load modeling more attractive to utilities and independent system operators (ISO's). They hypothesize and later demonstrate that the alternative will yield results comparable to that of traditional methods. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Power system modeling Load modeling nonlinear optimization methods Parameter estimation

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Modeling of coplanar waveguide meander-line inductors

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INTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING 2002年第6期12卷 520-529页

作者： Ho, KMJ Ellis, GA Ooi, BL Leong, MS Natl Univ Singapore Dept Elect & Comp Engn Singapore 117576 Singapore

A unique and simple method of modeling a coplanar waveguide meander-line inductor is presented. Using only the lower frequency response of electrically smaller inductors, their higher frequency response is predicted. In addition, the responses of physically larger inductors can also be made using circuit models synthesized directly from the unit cell layout of the inductors. The modeling and prediction results for an ideal metal and lossless substrate is presented, together with comparisons made for various lossy parameters. (C) 2002 Wiley Periodicals, Inc.

关键词： coplanar waveguide meander-line inductors circuit modeling computer-aided design environment nonlinear optimization methods

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Optimal design of a 7 T highly homogeneous superconducting magnet for a Penning trap

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中国物理C（英文版） 2010年第7期34卷 978-982页

作者： WU Wei HE Yuan MA Li-Zhen HUANG Wen-Xue XIA Jia-Wen Institute of Modern Physics Chinese Academy of Sciences Lanzhou 730000 China Graduate University of Chinese Academy of Sciences Beijing 100049 China Institute of Modern Physics Chinese Academy of Sciences Lanzhou 730000 China

A Penning trap system called Lanzhou Penning Trap (LPT) is now being developed for precise mass measurements at the Institute of Modern Physics (IMP). One of the key components is a 7 T actively shielded superconducting magnet with a clear warm bore of 156 mm. The required field homogeneity is 3×10-7 over two 1 cubic centimeter volumes lying 220 mm apart along the magnet axis. We introduce a two-step method which combines linear programming and a nonlinear optimization algorithm for designing the multi-section superconducting magnet. This method is fast and flexible for handling arbitrary shaped homogeneous volumes and coils. With the help of this method an optimal design for the LPT superconducting magnet has been obtained.

关键词： Penning trap linear programming magnet design nonlinear optimization methods pattern search

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nonlinear optimization and support vector machines

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ANNALS OF OPERATIONS RESEARCH 2022年第1期314卷 15-47页

作者： Piccialli, Veronica Sciandrone, Marco Sapienza Univ Roma Dipartimento Ingn Informat Automat & Gest A Ruber Via Ariosto 25 I-00185 Rome Italy

Support vector machine (SVM) is one of the most important class of machine learning models and algorithms, and has been successfully applied in various fields. nonlinear optimization plays a crucial role in SVM methodology, both in defining the machine learning models and in designing convergent and efficient algorithms for large-scale training problems. In this paper we present the convex programming problems underlying SVM focusing on supervised binary classification. We analyze the most important and used optimization methods for SVM training problems, and we discuss how the properties of these problems can be incorporated in designing useful algorithms.

关键词： Statistical learning theory Support vector machine Convex quadratic programming Wolfe's dual theory Kernel functions nonlinear optimization methods

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On reductibility of degenerate optimization problems to regular operator equations

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2016年第12期56卷 1992-2000页

作者： Bednarczuk, E. M. Tretyakov, A. A. Dorodnicyn Comp Ctr FRC CSC JL4S Moscow Russia Siedlce Univ Nat Sci Siedlce Poland Syst Res Inst Ul Newelska 6 Warsaw Poland

We present an application of the p-regularity theory to the analysis of non-regular (irregular, degenerate) nonlinear optimization problems. The p-regularity theory, also known as the p-factor analysis of nonlinear mappings, was developed during last thirty years. The p-factor analysis is based on the construction of the p-factor operator which allows us to analyze optimization problems in the degenerate case. We investigate reducibility of a non-regular optimization problem to a regular system of equations which do not depend on the objective function. As an illustration we consider applications of our results to non-regular complementarity problems of mathematical programming and to linear programming problems.

关键词： degenerate problems p-regularity nonlinear optimization methods

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nonlinear-PROGRAMMING SOLUTIONS TO THE NONSTATIONARY MARKOV MODEL

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 1986年第4期15卷 1169-1190页

作者： KELTON, CML SMITH, MA Department of Economics Wayne State University Detroit Michigan 48202 United States

A nonstationary Markov process model with embedded explanatory variables offers a means to account for underlying causal factors while retaining unrestrictive assumptions and the predictive ability of a stochastic framework. We find that a direct search algorithm requiring minimal user preparation is a feasible computational procedure for estimating such a model. We compare this method with several others using factorially designed Monte Carlo simulations and find evidence that a small state space and a long time series lead to better algorithmic performance.

关键词： nonlinear optimization methods aggregate frequency data stochastic processes

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nonlinear optimization and support vector machines

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4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH 2018年第2期16卷 111-149页

作者： Piccialli, Veronica Sciandrone, Marco Univ Roma Tor Vergata Dipartimento Ingn Civile & Ingn Informat Via Politecn I-100133 Rome Italy Univ Florence Dipartimento Ingn Informaz Via Santa Marta 3 I-50139 Florence Italy

Support Vector Machine (SVM) is one of the most important class of machine learning models and algorithms, and has been successfully applied in various fields. nonlinear optimization plays a crucial role in SVM methodology, both in defining the machine learning models and in designing convergent and efficient algorithms for large-scale training problems. In this paper we present the convex programming problems underlying SVM focusing on supervised binary classification. We analyze the most important and used optimization methods for SVM training problems, and we discuss how the properties of these problems can be incorporated in designing useful algorithms.

关键词： Statistical learning theory Support vector machine Convex quadratic programming Wolfe's dual theory Kernel functions nonlinear optimization methods

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Design of Open High Magnetic Field MRI Superconducting Magnet With Continuous Current and Genetic Algorithm Method

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IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY 2009年第3期19卷 2289-2292页

作者： Wang, Qiuliang Xu, Guoxin Dai, Yinming Zhao, Baozhi Yan, Luguang Kim, Keeman Chinese Acad Sci Inst Elect Engn Beijing Peoples R China Natl Fus Res Inst Taejon 305806 South Korea

An optimization design method of short-length actively shielded and open structure superconducting MRI magnets is suggested in the paper. Firstly, the section of the solenoid coil is simplified as a current loop with zero section to solve a linear programming problem. The position coordinates in the radius and axial, and current for the loop can be calculated by the linear programming method. Then, the cross-section of the coil is optimized with a genetic algorithm to get appropriate section size. The method of linear programming, especially combining with genetic algorithm, reduces optimizing variables, which makes the design of a magnet feasible. Based on the method, a full open MRI superconducting magnet is designed with maximum radii of 0.8 m and 1.2 m. In the paper, the detailed optimization technologies are presented.

关键词： Magnetic resonance imaging (MRI) nonlinear optimization methods open structure MRI magnet design

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Phase Estimation for Differential Interference Contrast Microscopy

Phase Estimation for Differential Interference Contrast Micr...

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作者： Lola Xiomara BAUTISTA ROZO UNIVERSITY COTE D'AZUR

学位级别：博士

In this dissertation we address the problem of estimating the phase from color images acquired with differential–interference–contrast (DIC) microscopy. This technique has been widely recognized for producing high contrast images at high lateral resolution. One of its disadvantages is that the observed images cannot be easily used for topographical and morphological interpretation, because the changes in phase of the light, produced by variations in the refractive index of the object, are hidden in the intensity image. We present an image formation model for polychromatic light, along with a detailed description of the point spread function (PSF). As for the phase recovery problem, we followed the inverse problem approach by means of minimizing a non-linear least–squares (LS)–like discrepancy term with an edge–preserving regularizing term, given by either the hypersurface (HS) potential or the total variation (TV) one. We investigate the analytical properties of the resulting objective non-convex functions, prove the existence of minimizers and propose a compact formulation of the gradient allowing fast computations. Then we use recent effective optimization tools able to obtain in both the smooth and the non-smooth cases accurate reconstructions with a reduced computational demand. We performed different numerical tests on synthetic realistic images and we compared the proposed methods with both the original conjugate gradient method proposed in the literature, exploiting a gradient–free linesearch for the computation of the steplength parameter, and other standard conjugate gradient approaches. The results we obtained in this approach show that the performances of the limited memory gradient method used for minimizing the LS+HS functional are much better than those of the CG approaches in terms of number of function/gradient evaluations and, therefore, computational time. Then we also consider another formulation of the phase retrieval problem by means of minimiza

关键词： DIC microscopy phase estimation nonlinear optimization methods

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