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SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
, 2002
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 597 (24 self)
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available, and that the constraint gradients are sparse. We discuss
Application of the Theory of Optimal Experiments to Adaptive ElectromagneticInduction Sensing of Buried Targets
 IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 6, Issue
"... Abstract—Amobile electromagneticinduction (EMI) sensor is considered for detection and characterization of buried conducting and/or ferrous targets. The sensormay be placed on a robot and, here, we consider design of an optimal adaptivesearch strategy. A frequencydependent magneticdipole model i ..."
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Cited by 20 (4 self)
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Abstract—Amobile electromagneticinduction (EMI) sensor is considered for detection and characterization of buried conducting and/or ferrous targets. The sensormay be placed on a robot and, here, we consider design of an optimal adaptivesearch strategy. A frequencydependent magneticdipole model is used to characterize the target at EMI frequencies. The goal of the search is accurate characterization of the dipolemodel parameters, denotedby the vector; the target positionandorientationare a subset of. The sensor position and operating frequency are denoted by the parameter vector p and a measurement is represented by the pair ðp;OÞ, where O denotes theobserveddata. Theparameters p are fixed for agivenmeasurement, but, in thecontext of a sequenceofmeasurements pmay bechangedadaptively. In a locally optimal sequenceofmeasurements,wedesire theoptimal sensor parameters,pNþ1 for estimationof, based on the previous measurements ðpn; OnÞn1;N. The search strategy is based on the theory of optimal experiments, as discussed in detail and demonstrated via several numerical examples. Index Terms—Optimal experiment, sensing, adaptive processing. 1
A New Hessian Preconditioning Method Applied to Variational Data Assimilation Experiments Using NASA General Circulation Models
, 1996
"... An analysis is provided to show that Courtier's et al. method for estimating the Hessian preconditioning is not applicable to important categories of cases involving nonlinearity. An extension of the method to cases with higher nonlinearity is proposed in the present paper by designing an alg ..."
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Cited by 17 (6 self)
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An analysis is provided to show that Courtier's et al. method for estimating the Hessian preconditioning is not applicable to important categories of cases involving nonlinearity. An extension of the method to cases with higher nonlinearity is proposed in the present paper by designing an algorithm that reduces errors in Hessian estimation induced by lack of validity of the tangent linear approximation. The new preconditioning method was numerically tested in the framework of variational data assimilation expeximents using both the National Aeronautics and Space Administration (NASA) semiLagrangian semiimplicit global shallowwater equations model and the adiabatic version of the NASA/Data AssimilatiOn Office (DAO) Goddard Observing System Version I (GEOS1) general circulation model. The authors' results show that the new preconditioning method speeds up convergence rate of minimization when applied to variational data assimilation cases characterized by strong nonlinearity. Finally,
SecondOrder Information in Data Assimilation
, 2002
"... In variational data assimilation (VDA) for meteorological and/or oceanic models, the assimilated fields are deduced by combining the model and the gradient of a cost functional measuring discrepancy between model solution and observation, via a firstorder optimality system. However, existence and ..."
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Cited by 16 (4 self)
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In variational data assimilation (VDA) for meteorological and/or oceanic models, the assimilated fields are deduced by combining the model and the gradient of a cost functional measuring discrepancy between model solution and observation, via a firstorder optimality system. However, existence and uniqueness of the VDA problem along with convergence of the algorithms for its implementation depend on the convexity of the cost function. Properties of local convexity can be deduced by studying the Hessian of the cost function in the vicinity of the optimum. This shows the necessity of secondorder information to ensure a unique solution to the VDA problem.
Solving Variational Inequalities with Monotone Operators on Domains Given by Linear Minimization Oracles
, 2015
"... ..."
Executive Summary
, 2007
"... All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publishers. ii Contents ..."
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All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publishers. ii Contents
Global Solutions for Nonlinear Systems Using Qualitative Reasoning*
"... This paper explores how qualitative information can be used to improve the performance of global optimization procedures. Specifically, we have constructed a nonlinear parameter estimation reasoner (NPER) for finding parameter values that match an ordinary differential equation (ODE) model to observ ..."
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This paper explores how qualitative information can be used to improve the performance of global optimization procedures. Specifically, we have constructed a nonlinear parameter estimation reasoner (NPER) for finding parameter values that match an ordinary differential equation (ODE) model to observed data. Qualitative reasoning (QR) is used within the NPER, for instance, to intelligently choose starting values for the unknown parameters and to empirically determine when the system appears to be chaotic. This enables odrpack, the nonlinear leastsquares solver that lies at the heart of this NPER, to avoid terminating at local extrema in the regression landscape. odrpack is uniquely suited to this task because of its efficiency and stability. The NPER's robustness is demonstrated via a Monte Carlo analysis ofsimulated examples drawn from across the domain of dynamics, including systems that are nonlinear, chaotic, and noisy. It is shown to locate solutions for noisy, incomplete realworld sensor datafrom radiocontrolled carsused in the University of British Columbia's soccerplaying robot project. The parameter estimation scheme described in this paper is a component of pret, an implemented computer program that uses a variety of artificial intelligence techniques to automate system identificationthe process ofinferring an internal ODE model from external ob
q1997 American Meteorological Society
"... The adjoint Newton algorithm (ANA) is based on the first and secondorder adjoint techniques allowing one to obtain the "Newton line search direction" by integrating a "tangent linear model" backward in time (with negative time steps). Moreover, the ANA provides a new techniqu ..."
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The adjoint Newton algorithm (ANA) is based on the first and secondorder adjoint techniques allowing one to obtain the "Newton line search direction" by integrating a "tangent linear model" backward in time (with negative time steps). Moreover, the ANA provides a new technique to find Newton line search direction without using gradient information. The error present in approximating the Hessian (the matrix of secondorder derivatives) of the cost function with respect to the control variables in the quasiNewtontype algorithm is thus completely eliminated, while the storage problem related to storing the Hessian no longer exists since the explicit Hessian is not required in this algorithm. The ANA is applied here, for the first time, in the framework of 4D variational data assimilation to the adiabatic version of the Advanced Regional Prediction System, a threedimensional, compressible, nonhydrostatic stormscale model. The purpose is to assess the feasibility and efficiency of the ANA as a largescale minimization algorithm in the setting of 4D variational data assimilation.
The Best Approximation of Radar Signal Amplitude and Delay
"... The estimation ofreceiver signal amplitude and delay, which can be converted to target cross section and range, is oneofthe fundamental functions ofsignal processing algorithms in a narrowband radar. The problem of tracking highearthorbit (HEO) satellites with groundbased radars requires a genera ..."
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The estimation ofreceiver signal amplitude and delay, which can be converted to target cross section and range, is oneofthe fundamental functions ofsignal processing algorithms in a narrowband radar. The problem of tracking highearthorbit (HEO) satellites with groundbased radars requires a generalization of simple filterbank signal processing architectures traditionally used to estimate signal amplitude and delay. A solution of the mathematical bestapproximation problem leads to a new signal processing architecture that efficiently estimates signal amplitude and delay in all of the generality necessary to address the BEO satellite tracking problem. Narrowbandradars capableoftrackinghighearthorbit (HEO) satellites are an important resource for both present and future space missions. To track satellites, the United States maintains a worldwide network of groundbased sensors that provide data for civilian and government users. At any given time, one or