Limited‐memory quasi‐Newton constrained inversion of 1D fixed‐wing airborne TEM data

2011 ◽  
Author(s):  
Lifeng Mao ◽  
Xuben Wang ◽  
Wenjie Li ◽  
Hanyu Lu
Keyword(s):  
Limited Memory ◽  
Quasi Newton

scholarly journals 3D magnetotelluric inversion using a limited-memory quasi-Newton optimization

Geophysics ◽  
2009 ◽  
Vol 74 (3) ◽  
pp. F45-F57 ◽  
Author(s):  
Dmitry Avdeev ◽  
Anna Avdeeva
Keyword(s):  
Penalty Function ◽  
Model Space ◽  
Nonlinear Inversion ◽  
Underground Structures ◽  
Usual Model ◽  
Limited Memory ◽  
Simple Bounds ◽  
Convergence Performance ◽  
Modeling Code ◽  
Quasi Newton

The limited-memory quasi-Newton method with simple bounds is used to develop a novel, fully 3D magnetotelluric (MT) inversion technique. This nonlinear inversion is based on iterative minimization of a classical Tikhonov regularized penalty function. However, instead of the usual model space of log resistivities, the approach iterates in a model space with simple bounds imposed on the conductivities of the 3D target. The method requires storage proportional to [Formula: see text], where [Formula: see text] is the number of conductivities to be recovered and [Formula: see text] is the number of correction pairs (practically, only a few). These requirements are much less than those imposed by other Newton methods, which usually require storage proportional to [Formula: see text] or [Formula: see text], where [Formula: see text] is the number of data to be inverted. The derivatives of the penalty function are calculated using an adjoint method based on electromagnetic field reciprocity. The inversion involves all four entries of the MT impedance matrix; the [Formula: see text] integral equation forward-modeling code is used as an engine for this inversion. Convergence, performance, and accuracy of the inversion are demonstrated on synthetic numerical examples. After investigating erratic resistivities in the upper part of the model obtained for one of the examples, we conclude that the standard Tikhonov regularization is not enough to provide consistently smooth underground structures. An additional regularization helps to overcome the problem.

scholarly journals Solving volterra integral equation via nonlinear programming

2016 ◽  
Vol 5 (4) ◽  
pp. 192
Author(s):  
Jamal Othman
Keyword(s):  
Integral Equation ◽  
Nonlinear Programming ◽  
Volterra Integral Equation ◽  
Least Square ◽  
Nonlinear Programming Problem ◽  
Programming Technique ◽  
New Approach ◽  
Nonlinear Volterra Integral Equation ◽  
Limited Memory ◽  
Quasi Newton

In this paper we propose an approach to find approximate solution to the nonlinear Volterra integral equation of the second type through a nonlinear programming technique by firstly converting the integral equation into a least square cost function as an objective function for an unconstrained nonlinear programming problem which solved by a nonlinear programming technique (The preconditioned limited- memory quasi-Newton conjugates, gradient method) and as far as we read this is a new approach in the ways of solving the nonlinear Volterra integral equation. We use Maple 11 software as a tool for performing the suggested steps in solving the examples.

scholarly journals The Adjoint Method for the Inverse Problem of Option Pricing

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Shou-Lei Wang ◽  
Yu-Fei Yang ◽  
Yu-Hua Zeng
Keyword(s):  
Inverse Problem ◽  
Option Pricing ◽  
Implied Volatility ◽  
Adjoint Method ◽  
Numerical Examples ◽  
Limited Memory ◽  
Minimization Procedure ◽  
Volatility Function ◽  
The Cost ◽  
Quasi Newton

The estimation of implied volatility is a typical PDE inverse problem. In this paper, we propose theTV-L1model for identifying the implied volatility. The optimal volatility function is found by minimizing the cost functional measuring the discrepancy. The gradient is computed via the adjoint method which provides us with an exact value of the gradient needed for the minimization procedure. We use the limited memory quasi-Newton algorithm (L-BFGS) to find the optimal and numerical examples shows the effectiveness of the presented method.

scholarly journals Parameters identification: an application to the Richards equation

2002 ◽  
Vol Volume 1, 2002 ◽  
Author(s):  
Pierre Ngnepieba ◽  
François Xavier Le Dimet ◽  
Alexis Boukong ◽  
Gabriel Nguetseng
Keyword(s):  
Standard Technique ◽  
Unconstrained Minimization ◽  
Richards Equation ◽  
Optimal Parameters ◽  
Scale Parameters ◽  
Limited Memory ◽  
Richards Model ◽  
International Audience ◽  
The One ◽  
Quasi Newton

International audience Inverse modeling has become a standard technique for estimating hydrogeologic parameters. These parameters are usually inferred by minimizing the sum of the squared differences between the observed system state and the one calculed by a mathematical model. Since some hydrodynamics parameters in Richards model cannot be measured, they have to be tuned with respect to the observation and the output of the model. Optimal parameters are found by minimizing cost function and the unconstrained minimization algorithm of the quasi-Newton limited memory type is used. The inverse model allows computation of optimal scale parameters and model sensi-tivity. La modélisation inverse est devenue une approche fréquemment utilisée pour l'estimation des paramètres en hydrogéologie. Fondamentalement cette technique est basée sur les méthodes de contrôle optimal qui nécessitent des observations et un modèle pour le calcul des dérivées du premier ordre. Le modèle adjoint du modèle de Richards est construit pour obtenir le gradient de la fonction coût par rapport aux paramètres de contrôle. Les paramètres hydrodynamiques sont pris comme paramètres de contrôle; leurs valeurs optimales sont trouvées en minimisant la fonction coût ceci en utilisant un algorithme de minimisation de type descente quasi-Newton. Cette approche est utilisée pour l'identification des paramètres hydrodynamiques sur un modèle d'écou-lement souterrain en zone non saturée, ainsi que les études de sensibilité du modèle.

scholarly journals A Newton-Like Trust Region Method for Large-Scale Unconstrained Nonconvex Minimization

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yang Weiwei ◽  
Yang Yueting ◽  
Zhang Chenhui ◽  
Cao Mingyuan
Keyword(s):  
Large Scale ◽  
Trust Region Method ◽  
Trust Region ◽  
Test Problems ◽  
Nonconvex Minimization ◽  
Trust Region Subproblem ◽  
Newton Equation ◽  
Limited Memory ◽  
Quasi Newton ◽  
Approximate Hessian

We present a new Newton-like method for large-scale unconstrained nonconvex minimization. And a new straightforward limited memory quasi-Newton updating based on the modified quasi-Newton equation is deduced to construct the trust region subproblem, in which the information of both the function value and gradient is used to construct approximate Hessian. The global convergence of the algorithm is proved. Numerical results indicate that the proposed method is competitive and efficient on some classical large-scale nonconvex test problems.

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