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Title: GMG - A guaranteed global optimization algorithm: Application to remote sensing

Abstract

We investigate the role of additional information in reducing the computational complexity of the global optimization problem (GOP). Following this approach, we develop GMG -- an algorithm to find the Global Minimum with a Guarantee. The new algorithm breaks up an originally continuous GOP into a discrete (grid) search problem followed by a descent problem. The discrete search identifies the basin of attraction of the global minimum after which the actual location of the minimizer is found upon applying a descent algorithm. The algorithm is first applied to the golf course problem, which serves as a litmus test for its performance in the presence of both complete and degraded additional information. GMG is further assessed on a set of standard benchmark functions. We then illustrate the performance of the the validated algorithm on a simple realization of the monocular passive ranging (MPR) problem in remote sensing, which consists of identifying the range of an airborne target (missile, plane, etc.) from its observed radiance. This inverse problem is set as a GOP whereby the difference between the observed and model predicted radiances is minimized over the possible ranges and atmospheric conditions. We solve the GOP using GMG and report on themore » performance of the algorithm.« less

Authors:
 [1];  [1];  [1];  [1]
  1. ORNL
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Center for Computational Sciences
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC)
OSTI Identifier:
930749
DOE Contract Number:
DE-AC05-00OR22725
Resource Type:
Journal Article
Resource Relation:
Journal Name: Mathematical and Computer Modelling; Journal Volume: 45; Journal Issue: 3-4
Country of Publication:
United States
Language:
English
Subject:
97; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; G CODES; PERFORMANCE; REMOTE SENSING; DATA ANALYSIS; RANGE FINDERS; ILLUMINANCE; TARGETS; global optimization; parameter identification; additional information; guaranteed global minimum; discrete search; remote sensing; monocular passive ranging

Citation Formats

D'Helon, Cassius, Protopopescu, Vladimir A, Wells, Jack C, and Barhen, Jacob. GMG - A guaranteed global optimization algorithm: Application to remote sensing. United States: N. p., 2007. Web. doi:10.1016/j.mcm.2006.06.005.
D'Helon, Cassius, Protopopescu, Vladimir A, Wells, Jack C, & Barhen, Jacob. GMG - A guaranteed global optimization algorithm: Application to remote sensing. United States. doi:10.1016/j.mcm.2006.06.005.
D'Helon, Cassius, Protopopescu, Vladimir A, Wells, Jack C, and Barhen, Jacob. Mon . "GMG - A guaranteed global optimization algorithm: Application to remote sensing". United States. doi:10.1016/j.mcm.2006.06.005.
@article{osti_930749,
title = {GMG - A guaranteed global optimization algorithm: Application to remote sensing},
author = {D'Helon, Cassius and Protopopescu, Vladimir A and Wells, Jack C and Barhen, Jacob},
abstractNote = {We investigate the role of additional information in reducing the computational complexity of the global optimization problem (GOP). Following this approach, we develop GMG -- an algorithm to find the Global Minimum with a Guarantee. The new algorithm breaks up an originally continuous GOP into a discrete (grid) search problem followed by a descent problem. The discrete search identifies the basin of attraction of the global minimum after which the actual location of the minimizer is found upon applying a descent algorithm. The algorithm is first applied to the golf course problem, which serves as a litmus test for its performance in the presence of both complete and degraded additional information. GMG is further assessed on a set of standard benchmark functions. We then illustrate the performance of the the validated algorithm on a simple realization of the monocular passive ranging (MPR) problem in remote sensing, which consists of identifying the range of an airborne target (missile, plane, etc.) from its observed radiance. This inverse problem is set as a GOP whereby the difference between the observed and model predicted radiances is minimized over the possible ranges and atmospheric conditions. We solve the GOP using GMG and report on the performance of the algorithm.},
doi = {10.1016/j.mcm.2006.06.005},
journal = {Mathematical and Computer Modelling},
number = 3-4,
volume = 45,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}
  • The monocular passive ranging (MPR) problem in remote sensing consists of identifying the precise range of an airborne target (missile, plane, etc.) from its observed radiance. This inverse problem may be set as a global optimization problem (GOP) whereby the difference between the observed and model predicted radiances is minimized over the possible ranges and atmospheric conditions. Using additional information about the error function between the predicted and observed radiances of the target, we developed GMG, a new algorithm to find the Global Minimum with a Guarantee. The new algorithm transforms the original continuous GOP into a discrete search problem,more » thereby guaranteeing to find the position of the global minimum in a reasonably short time. The algorithm is first applied to the golf course problem, which serves as a litmus test for its performance in the presence of both complete and degraded additional information. GMG is further assessed on a set of standard benchmark functions and then applied to various realizations of the MPR problem.« less
  • Remote sensing of the atmosphere from satellite to improve numerical weather prediction demands objective data handling methods, as the effectiveness of satellite data ultimately rests on our ability to process the data in real time. In this paper a procedure to recover high-resolution spectra from infrared Fourier spectrometer data is presented. The technique relies on the generalized cross-validation criterion and retains all the computational characteristics that are proper to the fast Fourier transform. The procedure yields adaptive apodizing functions that improve the convergence of the Fourier transform. Numerical examples are carried out using synthetic spectra computed by a high-resolution radiativemore » transfer code. The effect of additive noise is also analyzed. The application of the technique to remote sensing of the atmosphere is discussed. Although our applications of the method emphasize the problem of recovering radiance spectra from interferogram signals, the procedure also applied in a general context, for example, to the estimation of variance spectra of stochastic processes from their autocovariance functions. 14 refs., 5 figs., 4 tabs.« less
  • We present a general Global Minimization Algorithm (GMA) to identify basic or thermally coupled distillation configurations that require the least vapor duty under minimum reflux conditions for separating any ideal or near-ideal multicomponent mixture into a desired number of product streams. In this algorithm, global optimality is guaranteed by modeling the system using Underwood equations and reformulating the resulting constraints to bilinear inequalities. The speed of convergence to the globally optimal solution is increased by using appropriate feasibility and optimality based variable-range reduction techniques and by developing valid inequalities. As a result, the GMA can be coupled with already developedmore » techniques that enumerate basic and thermally coupled distillation configurations, to provide for the first time, a global optimization based rank-list of distillation configurations.« less
  • The oceans have a fundamental role in the global climate system because of their capacity to store and transport heat and absorb and emit trace gases which affect the earth's radiation budget. Although good progress has been made with issues such as carbon and sulfur cycling, feedback responses related to the impact of climate change on biological systems, and links between plankton ecology and climate, there is a lack of information on the distributions of biological properties on a global scale. This article reviews the potential contribution of ocean color measurements for biological studies within the context of climate change.more » The remote sensing of oceanic phytoplankton from satellites measuring radiance at visible and near infrared wavelenghts has produced a wealth of new information on biomass distributions and has provided a basis for new approaches to estimation of global marine primary productivity.« less
  • Remote sensing instruments for monitoring global changes are examined. The use of the earth observing system, a set of instrument platforms in polar, sun-synchoronous orbit that provide coverage of the entire globe, is discussed. The radar and imaging spectrometers utilized to obtain surface measurements are described. Atmospheric data is collected by the atmospheric IR sounder, the tropospheric emission spectrometer, and the stratospheric wind IR limb sounder. Consideration is given to the operation of the microwave limb sounder, the active cavity radiometer, and the TDRSS.