The SEISCOPE optimization toolbox: A large-scale nonlinear optimization library based on reverse communication

ABSTRACTThe SEISCOPE optimization toolbox is a set of FORTRAN 90 routines, which implement first-order methods (steepest-descent and nonlinear conjugate gradient) and second-order methods (l-BFGS and truncated Newton), for the solution of large-scale nonlinear optimization problems. An efficient line-search strategy ensures the robustness of these implementations. The routines are proposed as black boxes easy to interface with any computational code, where such large-scale minimization problems have to be solved. Traveltime tomography, least-squares migration, or full-waveform inversion are examples of such problems in the context of geophysics. Integrating the toolbox for solving this class of problems presents two advantages. First, it helps to separate the routines depending on the physics of the problem from the ones related to the minimization itself, thanks to the reverse communication protocol. This enhances flexibility in code development and maintenance. Second, it allows us to switch easily betw...

[1]  M. Hestenes,et al.  Methods of conjugate gradients for solving linear systems , 1952 .

[2]  C. M. Reeves,et al.  Function minimization by conjugate gradients , 1964, Comput. J..

[3]  E. Polak,et al.  Note sur la convergence de méthodes de directions conjuguées , 1969 .

[4]  J. Nocedal Updating Quasi-Newton Matrices With Limited Storage , 1980 .

[5]  T. Steihaug The Conjugate Gradient Method and Trust Regions in Large Scale Optimization , 1983 .

[6]  Guust Nolet,et al.  Seismic tomography : with applications in global seismology and exploration geophysics , 1987 .

[7]  Jorge Nocedal,et al.  A Numerical Study of the Limited Memory BFGS Method and the Truncated-Newton Method for Large Scale Optimization , 1991, SIAM J. Optim..

[8]  J. Virieux,et al.  Iterative asymptotic inversion in the acoustic approximation , 1992 .

[9]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[10]  Jorge Nocedal,et al.  A Limited Memory Algorithm for Bound Constrained Optimization , 1995, SIAM J. Sci. Comput..

[11]  Mrinal K. Sen,et al.  Global Optimization Methods in Geophysical Inversion , 1995 .

[12]  V. Eijkhout,et al.  Reverse Communication Interface for Linear Algebra Templates for Iterative Methods , 1995 .

[13]  Homer F. Walker,et al.  Choosing the Forcing Terms in an Inexact Newton Method , 1996, SIAM J. Sci. Comput..

[14]  Hicks,et al.  Gauss–Newton and full Newton methods in frequency–space seismic waveform inversion , 1998 .

[15]  Patrick R. Amestoy,et al.  Multifrontal parallel distributed symmetric and unsymmetric solvers , 2000 .

[16]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[17]  G. Schuster,et al.  Least-squares migration of incomplete reflection data , 1999 .

[18]  Nicholas I. M. Gould,et al.  Solving the Trust-Region Subproblem using the Lanczos Method , 1999, SIAM J. Optim..

[19]  Nicholas I. M. Gould,et al.  SOLVING THE TRUST-REGION SUBPROBLEM USING THE , 1999 .

[20]  Ya-Xiang Yuan,et al.  A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property , 1999, SIAM J. Optim..

[21]  S. Nash A survey of truncated-Newton methods , 2000 .

[22]  C. Shin,et al.  Improved amplitude preservation for prestack depth migration by inverse scattering theory , 2001 .

[23]  James C. Spall,et al.  Introduction to stochastic search and optimization - estimation, simulation, and control , 2003, Wiley-Interscience series in discrete mathematics and optimization.

[24]  Jean Charles Gilbert,et al.  Numerical Optimization: Theoretical and Practical Aspects , 2003 .

[25]  James C. Spall,et al.  Introduction to stochastic search and optimization - estimation, simulation, and control , 2003, Wiley-Interscience series in discrete mathematics and optimization.

[26]  S. Operto,et al.  Mixed‐grid and staggered‐grid finite‐difference methods for frequency‐domain acoustic wave modelling , 2004 .

[27]  R. Plessix A review of the adjoint-state method for computing the gradient of a functional with geophysical applications , 2006 .

[28]  J. Renaud Numerical Optimization, Theoretical and Practical Aspects— , 2006, IEEE Transactions on Automatic Control.

[29]  Gary Martin,et al.  Marmousi2 An elastic upgrade for Marmousi , 2006 .

[30]  James C. Spall,et al.  Introduction to Stochastic Search and Optimization. Estimation, Simulation, and Control (Spall, J.C. , 2007 .

[31]  Jean Virieux,et al.  An overview of full-waveform inversion in exploration geophysics , 2009 .

[32]  Yuhong Dai Nonlinear Conjugate Gradient Methods , 2011 .

[33]  S. Operto,et al.  Toward Gauss-Newton and Exact Newton Optimization for Full Waveform Inversion , 2012 .

[34]  Ludovic Métivier,et al.  Full Waveform Inversion and the Truncated Newton Method , 2013, SIAM J. Sci. Comput..

[35]  Ludovic Métivier,et al.  Fast Full Waveform Inversion with Source Encoding and Second Order Optimization Methods , 2013 .

[36]  A. Baumstein POCS-based geophysical constraints in multi-parameter Full Wavefield Inversion , 2013 .

[37]  Ludovic Métivier,et al.  A guided tour of multiparameter full-waveform inversion with multicomponent data: From theory to practice , 2013 .

[38]  Ludovic Métivier,et al.  Two-dimensional permittivity and conductivity imaging by full waveform inversion of multioffset GPR data: a frequency-domain quasi-Newton approach , 2014 .

[39]  Ludovic Métivier,et al.  Full waveform inversion and the truncated Newton method: quantitative imaging of complex subsurface structures , 2014 .

[40]  J. Virieux,et al.  Measuring the misfit between seismograms using an optimal transport distance: application to full waveform inversion , 2016 .

[41]  Ajie Chu,et al.  A NONLINEAR CONJUGATE GRADIENT METHOD AND ITS GLOBAL CONVERGENCE ANALYSIS , 2016 .