U.S.-Japan Cooperative Science: Algorithms for Linear Programs Over Symmetric Cones

9910084蒙泰罗该奖项支持佐治亚理工学院的雷纳托·蒙泰罗教授和日本东京统计数学研究所的土屋隆教授之间为期三年的合作研究项目。研究人员将对对称锥上的线性规划的算法进行研究。大规模半定规划(SDP)问题在连续优化、矩阵分析、工程、统计和离散/组合优化等领域有着广泛的应用，因此开发快速可靠的算法来求解SDP问题是非常重要的。这项研究的目的是为原始-对偶内点算法的行为提供新的见解，并开发新的计算工具，使实践者能够解决大规模的SDP问题。研究人员将研究解决大规模特殊结构SDP问题的非线性规划类型的算法。他们还将研究新的方法，以提高内点方法的计算性能，以解决大规模的SDP问题。最后，他们计划开发和实现有效的内点方法来解决非线性SDP问题。该项目汇集了两个拥有互补专业知识和研究能力的实验室的努力。这一研究项目具有极大的潜力，将对日益增长的关于(SDP)问题的文献以及开发有效的方法来解决这些问题产生强大的影响。它还将导致新的或改进的算法，以找到大规模优化问题的准确或近似解决方案，这些问题出现在工业、金融科学和工程的不同应用中。该项目通过一名研究生的参与促进国际人力资源的发展。通过思想和技术的交流，这个项目将扩大我们的基础知识基础，促进国际理解与合作。研究结果将发表在国际科学期刊上，并在美国和国外的科学会议上公布。

9910084MonteiroThis award supports a three-year collaborative research project between Professor Renato Monteiro of the Georgia Institute of Technology and Professor Takashi Tsuchiya at the Institute of Statistical Mathematics in Tokyo, Japan. The researchers will be undertaking a study of algorithms for linear programs over symmetric cones. Since large-scale semidefinite programming (SDP) problems arise in many applications in continuous optimization, matrix analysis, engineering, statistics and discrete/combinatorial optimization, it is of paramount importance to develop fast and reliable algorithms to solve them. The goal of the proposed research is to provide new insight into the behavior of primal-dual interior-point algorithms and to develop novel computational tools that will enable practitioners to solve large-scale SDP problems. The researchers will investigate nonlinear-programming-type algorithms for solving large-scale specially structured SDP problems. They will also be researching new methodologies to enhance the computational performance of interior-point methods towards solving large-scale SDP problems. Finally they plan to develop and implement efficient interior-point methods for solving nonlinear SDP problems. The project brings together the efforts of two laboratories that have complementary expertise and research capabilities. This research project has excellent potential to have a strong impact on the growing literature about (SDP) problems and on the development of efficient methods to solve them. It will also lead to new or improved algorithms to find exact or approximate solutions to large-scale optimization problems arising in diverse applications in industry, finance science, and engineering. The project advances international human resources through the participation of a graduate student. Through the exchange of ideas and technology, this project will broaden our base of basic knowledge and promote international understanding and cooperation. Results of the research will be published in international scientific journals and also presented at scientific meetings in the U.S. and abroad.