Scaled first–order methods for a class of large–scale constrained least square problems

2016 ◽  
Author(s):  
Vanna Lisa Coli ◽  
Valeria Ruggiero ◽  
Luca Zanni
Keyword(s):  
Large Scale ◽  
Least Square ◽  
First Order ◽  
Least Square Problems ◽  
First Order Methods

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

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. F1-F15 ◽  
Author(s):  
Ludovic Métivier ◽  
Romain Brossier
Keyword(s):  
Nonlinear Optimization ◽  
Large Scale ◽  
Convergence Rates ◽  
Optimization Problems ◽  
Waveform Inversion ◽  
Second Order ◽  
First Order ◽  
Truncated Newton ◽  
First Order Methods ◽  
Second Order Methods

The 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 ([Formula: see text]-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 between different optimization algorithms. In particular, it reduces the complexity related to the implementation of second-order methods. Because the latter benefit from faster convergence rates compared to first-order methods, significant improvements in terms of computational efforts can be expected.

scholarly journals First-Order Methods for Constrained Convex Programming Based on Linearized Augmented Lagrangian Function

2021 ◽  
Vol 3 (1) ◽  
pp. 89-117
Author(s):  
Yangyang Xu
Keyword(s):  
Large Scale ◽  
Augmented Lagrangian ◽  
Augmented Lagrangian Method ◽  
Linear Convergence ◽  
Classification Problem ◽  
Lagrangian Function ◽  
Augmented Lagrangian Function ◽  
Convex Programs ◽  
First Order ◽  
First Order Methods

First-order methods (FOMs) have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two FOMs for constrained convex programs, where the constraint set is represented by affine equations and smooth nonlinear inequalities. Both methods are based on the classical augmented Lagrangian function. They update the multipliers in the same way as the augmented Lagrangian method (ALM) but use different primal updates. The first method, at each iteration, performs a single proximal gradient step to the primal variable, and the second method is a block update version of the first one. For the first method, we establish its global iterate convergence and global sublinear and local linear convergence, and for the second method, we show a global sublinear convergence result in expectation. Numerical experiments are carried out on the basis pursuit denoising, convex quadratically constrained quadratic programs, and the Neyman-Pearson classification problem to show the empirical performance of the proposed methods. Their numerical behaviors closely match the established theoretical results.

scholarly journals Augmented Lagrangian–Based First-Order Methods for Convex-Constrained Programs with Weakly Convex Objective

2021 ◽  
Author(s):  
Zichong Li ◽  
Yangyang Xu
Keyword(s):  
Large Scale ◽  
Augmented Lagrangian ◽  
Proximal Point ◽  
First Order ◽  
Kkt Point ◽  
Large Scale Problems ◽  
Complexity Result ◽  
Linearly Constrained ◽  
First Order Methods ◽  
Better Than

First-order methods (FOMs) have been widely used for solving large-scale problems. A majority of existing works focus on problems without constraint or with simple constraints. Several recent works have studied FOMs for problems with complicated functional constraints. In this paper, we design a novel augmented Lagrangian (AL)–based FOM for solving problems with nonconvex objective and convex constraint functions. The new method follows the framework of the proximal point (PP) method. On approximately solving PP subproblems, it mixes the usage of the inexact AL method (iALM) and the quadratic penalty method, whereas the latter is always fed with estimated multipliers by the iALM. The proposed method achieves the best-known complexity result to produce a near Karush–Kuhn–Tucker (KKT) point. Theoretically, the hybrid method has a lower iteration-complexity requirement than its counterpart that only uses iALM to solve PP subproblems; numerically, it can perform significantly better than a pure-penalty-based method. Numerical experiments are conducted on nonconvex linearly constrained quadratic programs. The numerical results demonstrate the efficiency of the proposed methods over existing ones.

Assessing Medical Evidence

2018 ◽  
Author(s):  
Jacob Stegenga
Keyword(s):  
Quality Assessment ◽  
Randomized Trials ◽  
Empirical Studies ◽  
Allocation Concealment ◽  
Assessment Tools ◽  
Medical Evidence ◽  
Empirical Methods ◽  
First Order ◽  
First Order Methods

Medical scientists employ ‘quality assessment tools’ to assess evidence from medical research, especially from randomized trials. These tools are designed to take into account methodological details of studies, including randomization, subject allocation concealment, and other features of studies deemed relevant to minimizing bias. There are dozens of such tools available. They differ widely from each other, and empirical studies show that they have low inter-rater reliability and low inter-tool reliability. This is an instance of a more general problem called here the underdetermination of evidential significance. Disagreements about the quality of evidence can be due to different—but in principle equally good—weightings of the methodological features that constitute quality assessment tools. Thus, the malleability of empirical research in medicine is deep: in addition to the malleability of first-order empirical methods, such as randomized trials, there is malleability in the tools used to evaluate first-order methods.

scholarly journals Examination of Construct Validity and Criterion-Related Validity of the German Motor Test in Egyptian Schoolchildren

2021 ◽  
Vol 18 (16) ◽  
pp. 8341
Author(s):  
Osama Abdelkarim ◽  
Julian Fritsch ◽  
Darko Jekauc ◽  
Klaus Bös
Keyword(s):  
Construct Validity ◽  
Physical Fitness ◽  
Large Scale ◽  
Body Height ◽  
Cross Sectional Study ◽  
Latent Factors ◽  
Cross Sectional ◽  
First Order ◽  
Motor Test ◽  
Health Related

Physical fitness is an indicator for children’s public health status. Therefore, the aim of this study was to examine the construct validity and the criterion-related validity of the German motor test (GMT) in Egyptian schoolchildren. A cross-sectional study was conducted with a total of 931 children aged 6 to 11 years (age: 9.1 ± 1.7 years) with 484 (52%) males and 447 (48%) females in grades one to five in Assiut city. The children’s physical fitness data were collected using GMT. GMT is designed to measure five health-related physical fitness components including speed, strength, coordination, endurance, and flexibility of children aged 6 to 18 years. The anthropometric data were collected based on three indicators: body height, body weight, and BMI. A confirmatory factor analysis was conducted with IBM SPSS AMOS 26.0 using full-information maximum likelihood. The results indicated an adequate fit (χ2 = 112.3, df = 20; p < 0.01; CFI = 0.956; RMSEA = 0.07). The χ2-statistic showed significant results, and the values for CFI and RMSEA showed a good fit. All loadings of the manifest variables on the first-order latent factors as well as loadings of the first-order latent factors on the second-order superordinate factor were significant. The results also showed strong construct validity in the components of conditioning abilities and moderate construct validity in the components of coordinative abilities. GMT proved to be a valid method and could be widely used on large-scale studies for health-related fitness monitoring in the Egyptian population.

scholarly journals Simulations of a bubble wall interacting with an electroweak plasma

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Zong-Gang Mou ◽  
Paul M. Saffin ◽  
Anders Tranberg
Keyword(s):  
Large Scale ◽  
Baryon Asymmetry ◽  
Winding Number ◽  
Bubble Wall ◽  
Electroweak Phase Transition ◽  
First Order ◽  
The Standard Model ◽  
Technical Details ◽  
Real Time Simulations ◽  
Chern Simons

Abstract We perform large-scale real-time simulations of a bubble wall sweeping through an out-of-equilibrium plasma. The scenario we have in mind is the electroweak phase transition, which may be first order in extensions of the Standard Model, and produce such bubbles. The process may be responsible for baryogenesis and can generate a background of primordial cosmological gravitational waves. We study thermodynamic features of the plasma near the advancing wall, the generation of Chern-Simons number/Higgs winding number and consider the potential for CP-violation at the wall generating a baryon asymmetry. A number of technical details necessary for a proper numerical implementation are developed.

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