Majorized iPADMM for Nonseparable Convex Minimization Models with Quadratic Coupling Terms

2021 ◽  
Author(s):  
Yumin Ma ◽  
Ting Li ◽  
Yongzhong Song ◽  
Xingju Cai
Keyword(s):  
Positive Definite ◽  
Convex Minimization ◽  
Original Function ◽  
Practical Applications ◽  
Alternating Direction ◽  
Speed Up ◽  
Sublinear Convergence Rate ◽  
Coupling Terms ◽  
Quadratic Coupling ◽  
Proximal Alternating Direction Method

In this paper, we consider nonseparable convex minimization models with quadratic coupling terms arised in many practical applications. We use a majorized indefinite proximal alternating direction method of multipliers (iPADMM) to solve this model. The indefiniteness of proximal matrices allows the function we actually solved to be no longer the majorization of the original function in each subproblem. While the convergence still can be guaranteed and larger stepsize is permitted which can speed up convergence. For this model, we analyze the global convergence of majorized iPADMM with two different techniques and the sublinear convergence rate in the nonergodic sense. Numerical experiments illustrate the advantages of the indefinite proximal matrices over the positive definite or the semi-definite proximal matrices.

scholarly journals Dynamic maintenance model for high average-utility pattern mining with deletion operation

2021 ◽  
Author(s):  
Jimmy Ming-Tai Wu ◽  
Qian Teng ◽  
Shahab Tayeb ◽  
Jerry Chun-Wei Lin
Keyword(s):  
Pattern Mining ◽  
Computational Cost ◽  
Practical Applications ◽  
Itemset Mining ◽  
Dynamic Databases ◽  
Speed Up ◽  
Dynamic Maintenance ◽  
Average Utility ◽  
High Utility ◽  
Maintenance Model

AbstractThe high average-utility itemset mining (HAUIM) was established to provide a fair measure instead of genetic high-utility itemset mining (HUIM) for revealing the satisfied and interesting patterns. In practical applications, the database is dynamically changed when insertion/deletion operations are performed on databases. Several works were designed to handle the insertion process but fewer studies focused on processing the deletion process for knowledge maintenance. In this paper, we then develop a PRE-HAUI-DEL algorithm that utilizes the pre-large concept on HAUIM for handling transaction deletion in the dynamic databases. The pre-large concept is served as the buffer on HAUIM that reduces the number of database scans while the database is updated particularly in transaction deletion. Two upper-bound values are also established here to reduce the unpromising candidates early which can speed up the computational cost. From the experimental results, the designed PRE-HAUI-DEL algorithm is well performed compared to the Apriori-like model in terms of runtime, memory, and scalability in dynamic databases.

scholarly journals Service for parallel applications based on JINR cloud and HybriLIT resources

2019 ◽  
Vol 214 ◽  
pp. 07012 ◽  
Author(s):  
Nikita Balashov ◽  
Maxim Bashashin ◽  
Pavel Goncharov ◽  
Ruslan Kuchumov ◽  
Nikolay Kutovskiy ◽  
...  
Keyword(s):  
High Performance ◽  
Cloud Service ◽  
Parallel Applications ◽  
Cloud Infrastructure ◽  
Modular Architecture ◽  
Practical Applications ◽  
Speed Up ◽  
Scientific Results ◽  
Computational Resources ◽  
Performance Computing

Cloud computing has become a routine tool for scientists in many fields. The JINR cloud infrastructure provides JINR users with computational resources to perform various scientific calculations. In order to speed up achievements of scientific results the JINR cloud service for parallel applications has been developed. It consists of several components and implements a flexible and modular architecture which allows to utilize both more applications and various types of resources as computational backends. An example of using the Cloud&HybriLIT resources in scientific computing is the study of superconducting processes in the stacked long Josephson junctions (LJJ). The LJJ systems have undergone intensive research because of the perspective of practical applications in nano-electronics and quantum computing. In this contribution we generalize the experience in application of the Cloud&HybriLIT resources for high performance computing of physical characteristics in the LJJ system.

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