On the optimal linear convergence factor of the relaxed proximal point algorithm for monotone inclusion problems

Finding a zero of a maximal monotone operator is fundamental in convex optimization and monotone operator theory, and \emph{proximal point algorithm} (PPA) is a primary method for solving this problem. PPA converges not only globally under fairly mild conditions but also asymptotically at a fast linear rate provided that the underlying inverse operator is Lipschitz continuous at the origin. These nice convergence properties are preserved by a relaxed variant of PPA. Recently, a linear convergence bound was established in [M. Tao, and X. M. Yuan, J. Sci. Comput., 74 (2018), pp. 826-850] for the relaxed PPA, and it was shown that the bound is optimal when the relaxation factor $\gamma$ lies in $[1,2)$. However, for other choices of $\gamma$, the bound obtained by Tao and Yuan is suboptimal. In this paper, we establish tight linear convergence bounds for any choice of $\gamma\in(0,2)$ and make the whole picture about optimal linear convergence bounds clear. These results sharpen our understandings to the asymptotic behavior of the relaxed PPA.Comment: 9 pages and 1 figur

A Multi-Agent Evolutionary algorIthm for Connector-Based Assembly Sequence Planning

AbstractSome Evolutionary algorithms for connector-based ASP have been researched. But those algorithms have lots of blind searching because individuals have little intelligence in making use of geometry and assembly process information of product assembly body. To improve individuals’ intelligence, A multi-agent evolutionary algorithm for connector-based ASP (MAEA-ASP) is presented which is integrated with the multi-agent systems. learning, competition and crossover -mutation are designed as the behaviors of agent which locate lattice-like structure environment. Experimental results show that MAEA-ASP can find an approximate solution faster compared with other evolutionary algorithms

Role of tumor-associated macrophages in hepatocellular carcinoma: impact, mechanism, and therapy

Hepatocellular carcinoma (HCC) is a highly frequent malignancy worldwide. The occurrence and progression of HCC is a complex process closely related to the polarization of tumor-associated macrophages (TAMs) in the tumor microenvironment (TME). The polarization of TAMs is affected by a variety of signaling pathways and surrounding cells. Evidence has shown that TAMs play a crucial role in HCC, through its interaction with other immune cells in the TME. This review summarizes the origin and phenotypic polarization of TAMs, their potential impacts on HCC, and their mechanisms and potential targets for HCC immunotherapy

Integrated Analysis of Long Noncoding RNA and Coding RNA Expression in Esophageal Squamous Cell Carcinoma

Tumorigenesis is a complex dynamic biological process that includes multiple steps of genetic and epigenetic alterations, aberrant expression of noncoding RNA, and changes in the expression profiles of coding genes. We call the collection of those perturbations in genome space the “cancer initiatome.” Long noncoding RNAs (lncRNAs) are pervasively transcribed in the genome and they have key regulatory functions in chromatin remodeling and gene expression. Spatiotemporal variation in the expression of lncRNAs has been observed in development and disease states, including cancer. A few dysregulated lncRNAs have been studied in cancers, but the role of lncRNAs in the cancer initiatome remains largely unknown, especially in esophageal squamous cell carcinoma (ESCC). We conducted a genome-wide screen of the expression of lncRNAs and coding RNAs from ESCC and matched adjacent nonneoplastic normal tissues. We identified differentially expressed lncRNAs and coding RNAs in ESCC relative to their matched normal tissue counterparts and validated the result using polymerase chain reaction analysis. Furthermore, we identified differentially expressed lncRNAs that are co-located and co-expressed with differentially expressed coding RNAs in ESCC and the results point to a potential interaction between lncRNAs and neighboring coding genes that affect ether lipid metabolism, and the interaction may contribute to the development of ESCC. These data provide compelling evidence for a potential novel genomic biomarker of esophageal squamous cell cancer