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Sparse-spike seismic inversion with semismooth newton algorithm solver

SCIENTIFIC REPORTS 2024年第1期14卷 1-13页

作者： Dai, Ronghuo China West Normal Univ Sch Math & Informat Nanchong 637009 Peoples R China

Seismic prospecting has been widely used in the exploration and development of underground geological resources, such as mineral products (e.x., coal, uranium deposit), oil and gas, groundwater, and so forth. Seismic impedance is a physical characteristic parameter of underground formation, which can be used in lithologic classification, rock characterization, stratigraphic correlation, and further mineral reservoir prediction, reserve estimation, and so forth. To estimate impedance from seismic data, one must perform reflectivity series inversion first. Under a simple exponential integration transformation, the reflectivity series can give the final estimated impedance. Sparse-spike seismic inversion is the most common method to obtain reflectivity series with high resolution. It adopts a sparse regularization to impose sparsity on reflectivity series. From sparse reflectivity series, the final estimated impedance has blocky features to make formation interfaces and geological edges precise, which is very important to accurately delineate the distribution range of mineral resources. The development of sparse-spike seismic inversion is still facing major challenges of fast optimization algorithms in real-life application, especially for massive seismic data in 3D case. semismooth newton algorithm (SNA), which is a second order mehtod and has super-linear, even quadratic convergence rate, is used to solve sparse-spike seismic inversion. The proposed algorithm has been compared with common used algorithms through a synthetic seismic trace and a 3D real seismic data volume. The results show that the proposed algorithm has faster convergence rate and fewer computation time. It provides a new effective algorithm to solve sparse-spike seismic inversion.

关键词： Sparse-spike inversion Seismic impedance semismooth newton algorithm Sparse regularization

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A semismooth newton based dual proximal point algorithm for maximum eigenvalue problem

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2023年第2期85卷 547-582页

作者： Liu, Yong-Jin Yu, Jing Fuzhou Univ Ctr Appl Math Fujian Prov Sch Math & Stat Fuzhou 350108 Fujian Peoples R China Fuzhou Univ Sch Math & Stat Fuzhou 350108 Fujian Peoples R China

The maximum eigenvalue problem is to minimize the maximum eigenvalue function over an affine subspace in a symmetric matrix space, which has many applications in structural engineering, such as combinatorial optimization, control theory and structural design. Based on classical analysis of proximal point (Ppa) algorithm and semismooth analysis of nonseparable spectral operator, we propose an efficient semismooth newton based dual proximal point (Ssndppa) algorithm to solve the maximum eigenvalue problem, in which an inexact semismooth newton (Ssn) algorithm is applied to solve inner subproblem of the dual proximal point (d-Ppa) algorithm. Global convergence and locally asymptotically superlinear convergence of the d-Ppa algorithm are established under very mild conditions, and fast superlinear or even quadratic convergence of the Ssn algorithm is obtained when the primal constraint nondegeneracy condition holds for the inner subproblem. Computational costs of the Ssn algorithm for solving the inner subproblem can be reduced by fully exploiting low-rank or high-rank property of a matrix. Numerical experiments on max-cut problems and randomly generated maximum eigenvalue optimization problems demonstrate that the Ssndppa algorithm substantially outperforms the Sdpnal+ solver and several state-of-the-art first-order algorithms.

关键词： Maximum eigenvalue problem Proximal point algorithm semismooth newton algorithm Density matrix Quadratic growth condition

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A semismooth newton-based Augmented Lagrangian algorithm for Density Matrix Least Squares Problems

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2022年第3期195卷 749-779页

作者： Liu, Yong-Jin Yu, Jing Fuzhou Univ Ctr Appl Math Fujian Prov Sch Math & Stat Fuzhou 350108 Fujian Peoples R China Fuzhou Univ Sch Math & Stat Fuzhou 350108 Fujian Peoples R China

The density matrix least squares problem arises from the quantum state tomography problem in experimental physics and has many applications in signal processing and machine learning, mainly including the phase recovery problem and the matrix completion problem. In this paper, we first reformulate the density matrix least squares problem as an equivalent convex optimization problem and then design an efficient semismooth newton-based augmented Lagrangian (Ssnal) algorithm to solve the dual of its equivalent form, in which an inexact semismooth newton (Ssn) algorithm with superlinear or even quadratic convergence is applied to solve the inner subproblems. Theoretically, the global convergence and locally asymptotically superlinear convergence of the Ssnal algorithm are established under very mild conditions. Computationally, the costs of the Ssn algorithm for solving the subproblem are significantly reduced by making full use of low-rank or high-rank property of optimal solutions of the density matrix least squares problem. In order to verify the performance of our algorithm, numerical experiments conducted on randomly generated quantum state tomography problems and density matrix least squares problems with real data demonstrate that the Ssnal algorithm is more effective and robust than the Qsdpnal solver and several state-of-the-art first-order algorithms.

关键词： Density matrix least squares problems semismooth newton algorithm Augmented Lagrangian algorithm Quadratic growth condition

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Nonlinearly preconditioned semismooth newton algorithms for nonlinear nonsmooth systems

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2024年第6期101卷 601-622页

作者： Yang, Haijian Ma, Tian-Hao Hwang, Feng-Nan Cai, Xiao-Chuan Hunan Univ Chongqing Res Inst Chongqing Peoples R China Humanitas Univ Sch Math Changsha Peoples R China Univ Macau Dept Math Macau Peoples R China Natl Cent Univ Dept Math Taoyuan City 320317 Taiwan

We aim to develop efficient and robust algorithms for nonsmooth nonlinear systems arising from complementarity problems. The semismooth newton algorithm is popular due to its reliability and efficiency. However, it struggles with issues with imbalanced nonlinearities of the problems, leading to degraded convergence rates or failure despite help from the globalization techniques like linesearch or trust region. We introduce a right nonlinearly preconditioned semismooth newton algorithm to address this difficulty. The critical success ingredient is that before each global newton update, a nonlinear preconditioning step implicitly removes the so-called 'bad components' causing trouble via nonlinear subspace correction, inspired by Gaussian elimination but adapted nonlinearly to balance system nonlinearities. Additionally, our method integrates with a domain decomposition framework, enhancing parallelism. Numerical results on two classes of problems demonstrate significantly improved convergence over standard semismooth newton methods.

关键词： semismooth newton algorithm nonlinear preconditioning flow control complementarity problems parallel computing

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An Inexact semismooth newton-Based Augmented Lagrangian algorithm for Multi-Task Lasso Problems

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2024年第3期41卷 2350027-2350027页

作者： Lin, Lanyu Liu, Yong-Jin Fuzhou Univ Sch Math & Stat Fuzhou 350108 Peoples R China Fuzhou Univ Ctr Appl Math Fujian Prov Sch Math & Stat Fuzhou 350108 Peoples R China

This paper is concerned with the l(1),infinity-norm ball constrained multi-task learning problem, which has received extensive attention in many research areas such as machine learning, cognitive neuroscience, and signal processing. To address the challenges of solving large-scale multi-task Lasso problems, this paper develops an inexact semismooth newton-based augmented Lagrangian (Ssnal) algorithm. When solving the inner problems in the Ssnal algorithm, the semismooth newton (Ssn) algorithm with superlinear or even quadratic convergence is applied. Theoretically, this paper presents the global and asymptotically superlinear local convergence of the Ssnal algorithm under standard conditions. Computationally, we derive an efficient procedure to construct the generalized Jacobian of the projector onto l(1),infinity-norm ball, which is an important component of the Ssnal algorithm, making the computational cost in the Ssn algorithm very cheap. Comprehensive numerical experiments on the multi-task Lasso problems demonstrate that the Ssnal algorithm is more efficient and robust than several existing state-of-the-art first-order algorithms.

关键词： Multi-task Lasso problem augmented Lagrangian algorithm semismooth newton algorithm generalized Jacobian

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A semismooth newton method for nonlinear symmetric cone programming

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2012年第2期76卷 129-145页

作者： Kong, Lingchen Meng, Qingmin Beijing Jiaotong Univ Dept Appl Math Beijing 100044 Peoples R China Cent Hosp Taian Tai An 271000 Shandong Peoples R China

In this paper, we employ the projection operator to design a semismooth newton algorithm for solving nonlinear symmetric cone programming (NSCP). The algorithm is computable from theoretical standpoint and is proved t... 详细信息

关键词： Euclidean Jordan algebra Nonlinear symmetric cone programming semismooth newton algorithm Quadratical convergence

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An efficient algorithm for Fantope-constrained sparse principal subspace estimation problem

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APPLIED MATHEMATICS AND COMPUTATION 2024年 475卷

作者： Liu, Yong-Jin Wan, Yuqi Lin, Lanyu Fuzhou Univ Ctr Appl Math Fujian Prov Sch Math & Stat Fuzhou 350108 Fujian Peoples R China Fuzhou Univ Sch Math & Stat Fuzhou 350108 Fujian Peoples R China

The Fantope-constrained sparse principal subspace estimation problem is initially proposed Vu et al. (Vu et al., 2013). This paper investigates a semismooth newton based proximal point (P PASSN ) algorithm for solving the equivalent form of this problem, where a semismooth newton (S SN ) method is utilized to optimize the inner problems involved in the P PASSN algorithm. Under standard conditions, the P PASSN algorithm is proven to achieve global convergence and asymptotic superlinear convergence rate. Computationally, we derive nontrivial expressions the Fantope projection and its generalized Jacobian, which are key ingredients for the P PASSN algorithm. Some numerical results on synthetic and real data sets are presented to illustrate the effectiveness of the proposed P PASSN algorithm for large-scale problems and superiority over the alternating direction method of multipliers (ADMM).

关键词： Fantope projection semismooth newton algorithm Proximal point algorithm Generalized Jacobian

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A SENSITIVITY-BASED EXTRAPOLATION TECHNIQUE FOR THE NUMERICAL SOLUTION OF STATE-CONSTRAINED OPTIMAL CONTROL PROBLEMS

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ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS 2010年第3期16卷 503-522页

作者： Hintermueller, Michael Yousept, Irwin Humboldt Univ Dept Math D-10099 Berlin Germany Graz Univ Inst Math & Sci Comp A-8010 Graz Austria Tech Univ Berlin Inst Math D-10623 Berlin Germany

Sensitivity analysis (with respect to the regularization parameter) of the solution of a class of regularized state constrained optimal control problems is performed. The theoretical results are then used to establish an extrapolation-based numerical scheme for solving the regularized problem for vanishing regularization parameter. In this context, the extrapolation technique provides excellent initializations along the sequence of reducing regularization parameters. Finally, the favorable numerical behavior of the new method is demonstrated and a comparison to classical continuation methods is provided.

关键词： Extrapolation mixed control-state constraints PDE-constrained optimization semismooth newton algorithm sensitivity state constraints

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A Bilevel Optimization Approach for Parameter Learning in Variational Models

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SIAM JOURNAL ON IMAGING SCIENCES 2013年第2期6卷 938-983页

作者： Kunisch, Karl Pock, Thomas Graz Univ Inst Math & Sci Comp A-8010 Graz Austria Graz Univ Technol Inst Comp Graph & Vis A-8010 Graz Austria

In this work we consider the problem of parameter learning for variational image denoising models. The learning problem is formulated as a bilevel optimization problem, where the lower-level problem is given by the variational model and the higher-level problem is expressed by means of a loss function that penalizes errors between the solution of the lower-level problem and the ground truth data. We consider a class of image denoising models incorporating l(p)-norm-based analysis priors using a fixed set of linear operators. We devise semismooth newton methods for solving the resulting nonsmooth bilevel optimization problems and show that the optimized image denoising models can achieve state-of-the-art performance.

关键词： regularization parameter image denoising learning theory nondifferentiable optimization bilevel optimization semismooth newton algorithm

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