Primal-Dual Method and Algorithm for large Scale Computation with Applications in Engineering Mechancis

大规模计算在工程力学中的应用的原对偶方法和算法

基本信息

项目摘要

ABSTRACT0514768Virginia Polytechnic Institute and State UniversityPrimal-Dual Method And Algorithm For Large Scale Computation With Applications In Engineering MechancisDavid Y. Gao (Virginia Tech)Abstract: Global optimization problems are widespread in the mathematical modelling of real world systems for a very broad range of applications. Due to the nonconvexity of the cost functions, many problems in global optimization are NP-hard. Traditional direct methods and local optimization procedures can not guarantee the identification of the global minima. On the other hand, duality theory and methods may provide potentially important influence on the solutions and algorithms for global optimization problems.The primary goal of this project is to develop a general canonical primal-dual method and its associated triality theory in global optimization. The project focuses on a general constrained global optimization problem, which arises directly from numerical discretization of a large class of nonconvex variational problems in engineering mechanics. The secondary goal is to advance the development of certain powerful primal-dual algorithms with concrete applications to nonconvex mechanics.The intellectual merit of the proposed work includes (1) a potentially powerful canonical dual transformation which can be used to formulate perfect dual problems (with zero duality gap); (2) an interesting triality theory which can serve as an optimality criterion to identify both global minima and local extrema of nonconvex function. Each of these aspects presents its own challenges. Formulation of perfect dual problems requires nonstandard methods, as the traditional duality theory in convex analysis may lead to a so-called duality gap when the primal problem is nonconvex. Global optimality criterion for nonconvex/nonsmooth functions over feasible spaces will need special mathematical techniques due to the loss of convexity and smoothness.The broader impacts of this project are potentially very great as the proposed problem arises in multi-disciplinary fields of global optimization, nonconvex/nonsmooth analysis, engineering mechanics, modern materials, mathematical physics, and scientific computation. The general methodology of canonical dual transformation and the beautiful triality theory will bridge the existing gaps among these fields. The broad distribution of software and publications (including a set of three volumes of Handbook of Duality Theory in Engineering Science to be published by Springer) will benefit practitioners and scientists across engineering, mathematics, physics, and computational science. Two international conferences on global optimization and nonconvex mechanics will be organized in 2005 and 2006, respectively. These conferences will open new trends in modern analysis, optimization, and engineering science. Furthermore, they will stimulate young faculty and students to venture into this rich domain of research. The proposed work will be carried out by an interdisciplinary team at Virginia Tech which includes both undergraduate and graduate students from math and engineering departments. The completion of this project will lay a ground work in global optimization, nonconvex mechanics, and computational science.
弗吉尼亚理工学院和州立大学大规模计算的原始-对偶方法和算法及其在工程机械中的应用高大卫·Y·高(弗吉尼亚理工大学)摘要:全局优化问题广泛存在于实际系统的数学建模中,应用范围非常广泛。由于代价函数的非凸性,全局优化中的许多问题都是NP难的。传统的直接方法和局部优化方法不能保证辨识出全局极小值。另一方面,对偶理论和方法可能会对全局优化问题的解和算法产生潜在的重要影响。本项目的主要目标是在全局优化中发展一种通用的规范原始-对偶方法及其相关的三重性理论。该项目主要研究工程力学中一大类非凸变分问题的数值离散化直接产生的一般约束全局优化问题。第二个目标是促进某些强大的原始-对偶算法的发展,并将其具体应用于非凸力学。所提出的工作的智力价值包括(1)潜在的强大的正则对偶变换,它可以用来描述完美对偶问题(具有零对偶间隙);(2)有趣的三重性理论,它可以作为识别非凸函数的全局极值和局部极值的最优性准则。每一个方面都提出了自己的挑战。完全对偶问题的描述需要非标准的方法,因为当原始问题是非凸的时,传统的凸分析中的对偶理论可能会导致所谓的对偶缺口。可行域上非凸/非光滑函数的全局最优性准则由于失去了凸性和光滑性,将需要特殊的数学技巧。由于所提出的问题涉及全局优化、非凸/非光滑分析、工程力学、现代材料、数学物理和科学计算等多学科领域,因此该项目的潜在影响非常大。典范对偶变换的一般方法论和美丽三位一体理论将弥合这些领域之间存在的差距。软件和出版物的广泛发行(包括由斯普林格出版的一套三卷的工程科学对偶性理论手册)将使工程、数学、物理和计算科学的从业者和科学家受益。2005年和2006年将分别举办两次关于全局优化和非凸力学的国际会议。这些会议将开启现代分析、优化和工程科学的新趋势。此外,它们将激励年轻的教职员工和学生冒险进入这一丰富的研究领域。这项拟议的工作将由弗吉尼亚理工大学的一个跨学科团队进行,该团队包括来自数学和工程系的本科生和研究生。该项目的完成将为全局优化、非凸力学和计算科学奠定基础。

项目成果

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David Gao其他文献

Internal sequential commutation and single generation
内部顺序换向和单代
  • DOI:
  • 发表时间:
    2024
  • 期刊:
  • 影响因子:
    0
  • 作者:
    David Gao;Srivatsav Kunnawalkam Elayavalli;Gregory Patchell;Hui Tan
  • 通讯作者:
    Hui Tan
Data-driven motion correction rescues interpretation of rubidium PET scan with extreme breathing artifacts
  • DOI:
    10.1007/s12350-021-02814-4
  • 发表时间:
    2021-11-12
  • 期刊:
  • 影响因子:
    2.700
  • 作者:
    David Gao;Anahita Tavoosi;Christiane Wiefels;Azmina Merani;Kimberly Gardner;Bruce Spottiswoode;Charles Hayden;Rob Beanlands;Robert A. deKemp
  • 通讯作者:
    Robert A. deKemp
<strong>42099 Analysis of utilization of sun-protective behavior among national SPOT Skin Cancer® program screenees from 2018 to 2019</strong>
  • DOI:
    10.1016/j.jaad.2023.07.024
  • 发表时间:
    2023-09-01
  • 期刊:
  • 影响因子:
  • 作者:
    David Gao;Susan Swetter;Elena Hawryluk;Alan Geller;Derek Beaulieu
  • 通讯作者:
    Derek Beaulieu
Response to "Squamous Cell Carcinoma in Situ Achieves Tumor Clearance in More Mohs Stages Than Invasive Squamous Cell Carcinoma".
对“原位鳞状细胞癌比浸润性鳞状细胞癌在更多莫氏阶段实现肿瘤清除”的回应。
  • DOI:
  • 发表时间:
    2024
  • 期刊:
  • 影响因子:
    2.4
  • 作者:
    David Gao;David Ozog;Jesse Venesta
  • 通讯作者:
    Jesse Venesta
54535 Cost Savings with Non-excision-based Management of Keratoacanthoma: Insights from 386 Cases
  • DOI:
    10.1016/j.jaad.2024.07.673
  • 发表时间:
    2024-09-01
  • 期刊:
  • 影响因子:
  • 作者:
    David Gao;David Ozog;Jalal Maghfour;Qing-Sheng Mi;Jesse Veenstra
  • 通讯作者:
    Jesse Veenstra

David Gao的其他文献

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{{ truncateString('David Gao', 18)}}的其他基金

IUTAM Symposium on Duality, Complementarity and Symmetry in Nonlinear Mechanics
IUTAM 非线性力学对偶性、互补性和对称性研讨会
  • 批准号:
    0123932
  • 财政年份:
    2001
  • 资助金额:
    $ 18万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Duality Theory in Finite Deformation Nonsmooth Mechanics and Numerical Approaches
数学科学:有限变形非光滑力学中的对偶理论和数值方法
  • 批准号:
    9400565
  • 财政年份:
    1994
  • 资助金额:
    $ 18万
  • 项目类别:
    Standard Grant

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