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

该奖项支持佐治亚理工学院Renato Monteiro教授和日本东京统计数学研究所Takashi Tsuchiya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算法进行研究。由于大规模半定规划（SDP）问题在连续优化、矩阵分析、工程、统计和离散/组合优化等领域的许多应用中都存在，因此开发快速可靠的算法来解决这些问题至关重要。本研究的目标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，使从业者能够解决大规模的SDP问题。研究人员将研究求解大规模特殊结构SDP问题的非线性规划型算法。他们还将研究新的方法，以提高解决大规模SDP问题的内点方法的计算性能。最后，他们计划开发并实现求解非线性SDP问题的有效内点方法。该项目汇集了两个具有互补专业知识和研究能力的实验室的努力。本研究项目极有可能对越来越多的关于（SDP）问题的文献和解决这些问题的有效方法的发展产生重大影响。它还将导致新的或改进的算法，以找到精确或近似的解决方案，大规模优化问题出现在工业，金融科学和工程的各种应用。该项目通过研究生的参与促进了国际人力资源。通过思想和技术的交流，该项目将扩大我们的基础知识基础，促进国际了解与合作。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发表。

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.