An accelerated first-order regularized momentum descent ascent algorithm for stochastic nonconvex-concave minimax problems

Stochastic nonconvex minimax problems have attracted wide attention in machine learning, signal processing and many other fields in recent years. In this paper, we propose an accelerated first-order regularized momentum descent ascent algorithm (FORMDA) for solving stochastic nonconvex-concave minimax problems. The iteration complexity of the algorithm is proved to be $\tilde{\mathcal{O}}(\varepsilon ^{-6.5})$ to obtain an $\varepsilon$-stationary point, which achieves the best-known complexity bound for single-loop algorithms to solve the stochastic nonconvex-concave minimax problems under the stationarity of the objective function

A Unified Single-loop Alternating Gradient Projection Algorithm for Nonconvex-Concave and Convex-Nonconcave Minimax Problems

Much recent research effort has been directed to the development of efficient algorithms for solving minimax problems with theoretical convergence guarantees due to the relevance of these problems to a few emergent applications. In this paper, we propose a unified single-loop alternating gradient projection (AGP) algorithm for solving nonconvex-(strongly) concave and (strongly) convex-nonconcave minimax problems. AGP employs simple gradient projection steps for updating the primal and dual variables alternatively at each iteration. We show that it can find an $\varepsilon$-stationary point of the objective function in $\mathcal{O}\left( \varepsilon ^{-2} \right)$ (resp. $\mathcal{O}\left( \varepsilon ^{-4} \right)$) iterations under nonconvex-strongly concave (resp. nonconvex-concave) setting. Moreover, its gradient complexity to obtain an $\varepsilon$-stationary point of the objective function is bounded by $\mathcal{O}\left( \varepsilon ^{-2} \right)$ (resp., $\mathcal{O}\left( \varepsilon ^{-4} \right)$) under the strongly convex-nonconcave (resp., convex-nonconcave) setting. To the best of our knowledge, this is the first time that a simple and unified single-loop algorithm is developed for solving both nonconvex-(strongly) concave and (strongly) convex-nonconcave minimax problems. Moreover, the complexity results for solving the latter (strongly) convex-nonconcave minimax problems have never been obtained before in the literature

Local Reasoning about Probabilistic Behaviour for Classical-Quantum Programs

Verifying the functional correctness of programs with both classical and quantum constructs is a challenging task. The presence of probabilistic behaviour entailed by quantum measurements and unbounded while loops complicate the verification task greatly. We propose a new quantum Hoare logic for local reasoning about probabilistic behaviour by introducing distribution formulas to specify probabilistic properties. We show that the proof rules in the logic are sound with respect to a denotational semantics. To demonstrate the effectiveness of the logic, we formally verify the correctness of non-trivial quantum algorithms including the HHL and Shor's algorithms.Comment: 27 pages. arXiv admin note: text overlap with arXiv:2107.0080

Enterprise Recruitment System Designed to Study the Effectiveness of Indicators

The quality of the design for a company’s employing system index has a close relationship with a principle that the corporation whether can practice during the human resource employing or not. At present, the basic reason for low-effect in talents selection of a corporation in china is lack of a normative and scientific selection of talent effectiveness index system. This article is designed for a selection of talent effectiveness index system to help the corporation to select a talent who is fit for the development of the corporation, and to promote the stable and sustainable development of corporations

GASdb: a large-scale and comparative exploration database of glycosyl hydrolysis systems

<p>Abstract</p> <p>Background</p> <p>The genomes of numerous cellulolytic organisms have been recently sequenced or in the pipeline of being sequenced. Analyses of these genomes as well as the recently sequenced metagenomes in a systematic manner could possibly lead to discoveries of novel biomass-degradation systems in nature.</p> <p>Description</p> <p>We have identified 4,679 and 49,099 free acting glycosyl hydrolases with or without carbohydrate binding domains, respectively, by scanning through all the proteins in the UniProt Knowledgebase and the JGI Metagenome database. Cellulosome components were observed only in bacterial genomes, and 166 cellulosome-dependent glycosyl hydrolases were identified. We observed, from our analysis data, unexpected wide distributions of two less well-studied bacterial glycosyl hydrolysis systems in which glycosyl hydrolases may bind to the cell surface directly rather than through linking to surface anchoring proteins, or cellulosome complexes may bind to the cell surface by novel mechanisms other than the other used SLH domains. In addition, we found that animal-gut metagenomes are substantially enriched with novel glycosyl hydrolases.</p> <p>Conclusions</p> <p>The identified biomass degradation systems through our large-scale search are organized into an easy-to-use database GASdb at <url>http://csbl.bmb.uga.edu/~ffzhou/GASdb/</url>, which should be useful to both experimental and computational biofuel researchers.</p

Primal Dual Alternating Proximal Gradient Algorithms for Nonsmooth Nonconvex Minimax Problems with Coupled Linear Constraints

Nonconvex minimax problems have attracted wide attention in machine learning, signal processing and many other fields in recent years. In this paper, we propose a primal dual alternating proximal gradient (PDAPG) algorithm and a primal dual proximal gradient (PDPG-L) algorithm for solving nonsmooth nonconvex-strongly concave and nonconvex-linear minimax problems with coupled linear constraints, respectively. The corresponding iteration complexity of the two algorithms are proved to be $\mathcal{O}\left( \varepsilon ^{-2} \right)$ and $\mathcal{O}\left( \varepsilon ^{-3} \right)$ to reach an $\varepsilon$-stationary point, respectively. To our knowledge, they are the first two algorithms with iteration complexity guarantee for solving the two classes of minimax problems

Effect of Recession on the Re-entry Capsule Aerodynamic Characteristic

AbstractNumerical simulation and analysis of aerodynamic characteristics of Soyuz ablation shape is carried out in this paper for the adverse influence coming from recession. The result indicates that the shape change caused by the recession will increase absolute value of trim angle of attack and trim lift-drag ratio. The conclusion offers reference for the aerodynamic layout design and improve of the Soyuz re-entry capsule