A Semismooth Newton-CG Method for Constrained Parameter Identification in Seismic Tomography
نویسندگان
چکیده
Seismic tomography is a technique to determine the material properties of the Earth’s subsurface based on the observation of seismograms. This can be stated as a PDE-constrained optimization problem governed by the elastic wave equation. We present a semismooth Newton-PCG method with a trust-region globalization for full-waveform seismic inversion that uses a MoreauYosida regularization to handle additional constraints on the material parameters. We establish results on the differentiability of the parameter-to-state operator and analyze the proposed optimization method in a function space setting. The elastic wave equation is discretized by a high-order continuous Galerkin method in space and an explicit Newmark time-stepping scheme. The matrixfree implementation relies on the adjoint-based computation of the gradient and Hessian-vector products and on an MPI-based parallelization. Numerical results are shown for an application in geophysical exploration on reservoir-scale.
منابع مشابه
A Semismooth Newton-CG Dual Proximal Point Algorithm for Matrix Spectral Norm Approximation Problems
We consider a class of matrix spectral norm approximation problems for finding an affine combination of given matrices having the minimal spectral norm subject to some prescribed linear equality and inequality constraints. These problems arise often in numerical algebra, engineering and other areas, such as finding Chebyshev polynomials of matrices and fastest mixing Markov chain models. Based ...
متن کاملSemismooth Newton and Quasi-Newton Methods in Weighted l−Regularization of Nonlinear Inverse Problems
In this paper, we investigate the semismooth Newton and quasi-Newton methods for the minimization problem in the weighted `−regularization of nonlinear inverse problems. We propose the conditions for obtaining the convergence of two methods. The semismooth Newton method is proven to locally converge with superlinear rate and the semismooth quasi-Newton method is proven to locally converge at le...
متن کاملSDPNAL \(+\) : a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints
Abstract In this paper, we present a majorized semismooth Newton-CG augmented Lagrangian method, called SDPNAL+, for semidefinite programming (SDP) with partial or full nonnegative constraints on the matrix variable. SDPNAL+ is a much enhanced version of SDPNAL introduced by Zhao et al. (SIAM J Optim 20:1737–1765, 2010) for solving generic SDPs. SDPNAL works very efficiently for nondegenerate S...
متن کاملA Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise
متن کامل
A Newton-CG Augmented Lagrangian Method for Semidefinite Programming
We consider a Newton-CG augmented Lagrangian method for solving semidefinite programming (SDP) problems from the perspective of approximate semismooth Newton methods. In order to analyze the rate of convergence of our proposed method, we characterize the Lipschitz continuity of the corresponding solution mapping at the origin. For the inner problems, we show that the positive definiteness of th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Scientific Computing
دوره 37 شماره
صفحات -
تاریخ انتشار 2015