Advances in Mathematical Methods and High Performance Computing
暫譯: 數學方法與高效能計算的進展

本次會議的特刊將對研究人員和學術界人士有極大的幫助。在此次會議中，學者、技術專家和研究人員將有機會與應用數學和科學計算領域的知名人士互動。本次國際會議將涵蓋的主題非常全面，足以幫助與會者了解該領域的新發展和新興趨勢。在過去的二十年中，高效能計算（High-Performance Computing, HPC）系統在其架構設計上經歷了許多變化，以滿足日益增長的大規模科學計算需求。準確、快速且可擴展的性能模型和模擬工具對於評估大規模計算系統的替代架構設計決策至關重要。本次會議回顧了在HPC系統和應用的建模與模擬方面的一些影響力工作，識別了一些主要挑戰，並概述了我們認為對HPC建模和模擬社群至關重要的未來研究方向。

Vinai K Singh is the Professor of Mathematics in the Department of Applied Mathematics, Inderprastha Engineering College Ghaziabad, India. Dr. Singh holds a Ph. D degree. in Approximation Theory from Department of Applied Mathematics, Institute of Technology, Banaras Hindu University (Now IIT BHU), Varanasi, India. He has been actively engaged in research activity since 1997. His areas of research interest include functional analysis, approximation theory, and different kinds of positive operators. He is author of 3 book chapters and 6 books and over 29 research papers in the national and International Journals of repute. He referees articles for professional journals and serves as editorial member of many national and international journals.
David Y Gao is the Alexander Rubinov Chair Professor of Mathematics at the Federation University Australia. He is the author of 14 monograph, handbook, special volumes and more than 200 research papers (> 50% are single authored) on applied mathematics, theoretical and computational mechanics, global optimization and operations research etc. His main research contributions include a canonical duality-triality theory, several mathematical models in engineering mechanics and material science, a series of complete solutions to a class of nonconvex/nonsmooth/discrete problems in nonlinear sciences, and some deterministic methods/algorithms for solving certain NPhard problems in global optimization and computational science. One application of this canonical duality theory in large deformation solid mechanics solved a 50-years open problem and leads to a pure complementary energy principle (i.e. the Gao Principle in the literature), which has broad applications in engineering mechanics and physics. One of the large deformed beam models he proposed in 1996 is now recognized as the nonlinear Gao beam which can be used to study postbuckling analysis and plays an important role in real-world applications. In discrete systems, this canonical duality theory shows that the NP-hard 0-1 integer programming problems are identical to a continuous unconstrained Lipschitzian global optimization problem which can be solved deterministically. Professor Gao's multidisciplinary research has been supported continuously by different programs at US National Science Foundation (NSF) and US Air Force Office for Scientific Research (AFOSR) before he moved to Australia in 2010. He is one of a few researchers in the southern hemisphere who receive research grants every year directly from the AFOSR Washington Office. Recently, Professor Gao's canonical duality-triality theory has been identified by AFOSR as a breakthrough research and his team has win two prestigious international grant awards with total US$600,000 for 2016-2020.
Andreas Fischer is director of the Institute of Numerical Mathematics at TU Dresden. After his habilitation in 1998, he became an associate professor at the University of Dortmund. Since 2002, he holds the Chair of Numerical Optimization at TU Dresden. His research concentrates on topics around the design and analysis of efficient algorithms in the field of mathematical programming. With his group, he works on theoretical and applied problems in continuous and discrete optimization. For example, this includes generalized Nash equilibria, eigenvalue complementarity problems, beamforming for wireless board-to-board communication, resource allocation, parameter optimization in machine learning, or minimum connectivity inference problems. Currently, he is a principal investigator at the Collaborative Research Center Highly Adaptive Energy-efficient Computing (HAEC) and of further research projects. Andreas Fischer is in the editorial board of several international journals.

Vinai K Singh 是印度 Ghaziabad 的 Inderprastha 工程學院應用數學系的數學教授。Singh 博士擁有來自印度瓦拉納西的班納拉斯印度大學（現為 IIT BHU）應用數學系的近似理論博士學位。他自 1997 年以來積極參與研究活動。他的研究興趣包括函數分析、近似理論以及各種正算子。他是 3 本書章節和 6 本書的作者，以及在國內外知名期刊上發表的 29 篇以上的研究論文。他為專業期刊審稿，並擔任多本國內外期刊的編輯委員。

David Y Gao 是澳大利亞聯邦大學的 Alexander Rubinov 數學講座教授。他是 14 本專著、手冊、特刊以及 200 多篇研究論文的作者（超過 50% 為單獨作者），涵蓋應用數學、理論與計算力學、全局優化和運籌學等領域。他的主要研究貢獻包括一個典範對偶-三重性理論、幾個工程力學和材料科學中的數學模型、一系列針對非凸/非光滑/離散問題的完整解決方案，以及一些用於解決某些 NP-hard 問題的確定性方法/算法。在大型變形固體力學中，這一典範對偶理論的一個應用解決了一個持續 50 年的開放問題，並導致了一個純補充能量原則（即文獻中的 Gao 原則），在工程力學和物理學中具有廣泛的應用。他在 1996 年提出的一個大型變形梁模型現在被認可為非線性 Gao 梁，可用於研究後屈曲分析，並在現實應用中扮演重要角色。在離散系統中，這一典範對偶理論顯示 NP-hard 的 0-1 整數規劃問題與一個可以確定性解決的連續無約束 Lipschitzian 全局優化問題是相同的。Gao 教授的多學科研究得到了美國國家科學基金會（NSF）和美國空軍科學研究辦公室（AFOSR）不同計劃的持續支持，直到他在 2010 年移居澳大利亞。他是南半球少數每年直接從 AFOSR 華盛頓辦公室獲得研究資助的研究者之一。最近，Gao 教授的典範對偶-三重性理論被 AFOSR 確認為突破性研究，他的團隊在 2016-2020 年期間獲得了總額 60 萬美元的兩項國際著名研究資助獎。

Andreas Fischer 是德累斯頓工業大學數值數學研究所的所長。在 1998 年獲得資格認證後，他成為多特蒙德大學的副教授。自 2002 年以來，他在德累斯頓工業大學擔任數值優化講座教授。他的研究集中在數學規劃領域中高效算法的設計和分析上。他的團隊致力於連續和離散優化中的理論和應用問題。例如，這包括廣義 Nash 均衡、特徵值互補問題、無線板對板通信的波束形成、資源分配、機器學習中的參數優化或最小連通推斷問題。目前，他是高適應性節能計算（HAEC）合作研究中心的主要研究者以及其他研究項目的負責人。Andreas Fischer 是幾本國際期刊的編輯委員會成員。