Parallel Successive Convex Approximation for Nonsmooth Nonconvex Optimization

Consider the problem of minimizing the sum of a smooth (possibly non-convex) and a convex (possibly nonsmooth) function involving a large number of variables. A popular approach to solve this problem is the block coordinate descent (BCD) method whereby at each iteration only one variable block is updated while the remaining variables are held fixed. With the recent advances in the developments of the multi-core parallel processing technology, it is desirable to parallelize the BCD method by allowing multiple blocks to be updated simultaneously at each iteration of the algorithm. In this work, we propose an inexact parallel BCD approach where at each iteration, a subset of the variables is updated in parallel by minimizing convex approximations of the original objective function. We investigate the convergence of this parallel BCD method for both randomized and cyclic variable selection rules. We analyze the asymptotic and non-asymptotic convergence behavior of the algorithm for both convex and non-convex objective functions. The numerical experiments suggest that for a special case of Lasso minimization problem, the cyclic block selection rule can outperform the randomized rule

Exploring the mysteries of deep oil and gas formation in the South China Sea to guide Palaeocene exploration in the Pearl River Mouth Basin

Deep oil and gas resources in the South China Sea have drawn increasing attention in recent years, involving several essential challenges such as favorable zone prediction, deep burial, poor data quality, non-homogeneous reservoir properties, low drilling rate, and the low research degree of Paleozoic strata. These issues vastly affect the exploration and development of deep oil and gas resources in this area. Specifically, the Lufeng and Huizhou Depressions exhibit rich hydrocarbon accumulation and distribution areas in the Pearl River Mouth Basin, thereby possess great resource potential. The seven papers discussed here propose a set of practical techniques that can be applied to the exploration of deep Paleogene in the shallow layers of the Pearl River Mouth Basin. All of these works make important contributions deepening the theory of Paleogene reservoir formation and promoting further exploration of Paleogene in the Pearl River Mouth Basin, to increase the hydrocarbon storage and production prospects.Cited as: Pang, X., Li, H., Pang, H. Exploring the mysteries of deep oil and gas formation in the South China Sea to guide Palaeocene exploration in the Pearl River Mouth Basin. Advances in Geo-Energy Research, 2022, 6(5): 361-362. https://doi.org/10.46690/ager.2022.05.0

Practical Development Of An Open Architecture Personal Computer-Based Numerical Control (Oapc-Nc) System [TJ1189. P535 2005 f rb].

In this research, an open architecture personal computer-based numerical control (OAPC-NC) system that can generate G-code was developed. Dalam pengajian ini, satu sistem kawalan berarkitektur terbuka berdasarkan komputer perseorangan (OAPC-NC) yang dapat menjalankan kod kawalan berangka telah dicipta

Supersymmetric Solutions in Four-Dimensional Off-Shell Curvature-Squared Supergravity

Off-shell formulations of supergravities allow one to add closed-form higher-derivative super-invariants that are separately supersymmetric to the usual lower-derivative actions. In this paper we study four-dimensional off-shell N=1 supergravity where additional super-invariants associated with the square of the Weyl tensor and the square of the Ricci scalar are included. We obtain a variety of solutions where the metric describes domain walls, Lifshitz geometries, and also solutions of a kind known as gyratons. We find that in some cases the solutions can be supersymmetric for appropriate choices of the parameters. In some solutions the auxiliary fields may be imaginary. One may reinterpret these as real solutions in an analytically-continued theory. Since the supersymmetry transformation rules now require the gravitino to be complex, the analytically-continued theory has a "fake supersymmetry" rather than a genuine supersymmetry. Nevertheless, the concept of pseudo-supersymmetric solutions is a useful one, since the Killing spinor equations provide first-order equations for the bosonic fields.Comment: 28 page