Due to the rapid advance of general-purpose graphics processing unit (GPU), it is an active research topic to study performance improvement of non-linear optimization with parallel implementation on GPU, as attested by the much research on parallel implementation of relatively simple optimization methods, such as the conjugate gradient method. We study in this context the L-BFGS-B method, or th...

Limited memory quasi-Newton methods and trust-region methods represent two efficient approaches used for solving unconstrained optimization problems. A straightforward combination of them deteriorates the efficiency of the former approach, especially in the case of large-scale problems. For this reason, the limited memory methods are usually combined with a line search. We show how to efficient...

Alexander Rothkopf Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany (Dated: October 31, 2011) Abstract We propose an improvement to the implementation of the well established Maximum Entropy Method by taking into account carefully the role of prior information. This involves a departure from Bryan’s concept of search space, a change that becomes crucial for the success of ...

In this project, we study learning the Logistic Regression model by gradient ascent and stochastic gradient ascent. Regularization is used to avoid overfitting. Some practical tricks to improve learning are also explored, such as batch-based gradient ascent, data normalization, grid searching, early stopping, and model averaging. We observe the factors that affect the result, and determine thes...

In many learning tasks, structural models usually lead to better interpretability and higher generalization performance. In recent years, however, the simple structural models such as lasso are frequently proved to be insufficient. Accordingly, there has been a lot of work on “superposition-structured” models where multiple structural constraints are imposed. To efficiently solve these “superpo...

This letter addresses an intelligent reflecting surface (IRS) to the uplink nonorthogonal multiple access (NOMA) served by a multiantenna receiver for effective data collection from massive devices. We aim achieve max-min fairness of network optimizing receive beamforming, IRS reflection, and transmit power allocation (PA) For this purpose, first, we design block coordinate descent (BCD) algori...

The novel coronavirus disease, also known as COVID-19, is a disease outbreak that was first identified in Wuhan, Central Chinese city. In this report, short analysis focusing on Australia, Italy, and UK conducted. includes confirmed recovered cases deaths, the growth rate Australia compared with Italy UK, trend of different Australian regions. Mathematical approaches based susceptible, infected...

We extend the well-known BFGS quasi-Newton method and its memory-limited variant LBFGS to the optimization of nonsmooth convex objectives. This is done in a rigorous fashion by generalizing three components of BFGS to subdifferentials: the local quadratic model, the identification of a descent direction, and the Wolfe line search conditions. We prove that under some technical conditions, the re...

L-BFGS has been applied as an effective parameter estimation method for various machine learning algorithms since 1980s. With an increasing demand to deal with massive instances and variables, it is important to scale up and parallelize L-BFGS effectively in a distributed system. In this paper, we study the problem of parallelizing the L-BFGS algorithm in large clusters of tens of thousands of ...

The resistivity method and time-domain-induced polarization (TDIP) are two branches of electric exploration that used to solve problems in mineral exploration, hydrogeology engineering geology. In recent years, integrating different physical parameters for joint inversion improve the accuracy results has been extensively examined; however, three-dimensional methods above not realized. To furthe...