CAREER: Theoretical and Computational Advances for Enabling Robust Numerical Guarantees in Linear and Mixed Integer Programming Solvers

职业：在线性和混合整数规划求解器中实现鲁棒数值保证的理论和计算进展

• 批准号: 2340527
• 负责人: Adolfo Escobedo
• 金额: $ 56.16万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-08-15 至 2029-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2340527&HistoricalAwards=false
• 关键词: CAREER; Theoretical; Computational; Advances; Enabling

Mathematical programming is a systematic problem-solving approach that utilizes mathematical models and algorithms to make optimal decisions, subject to a given set of restrictions. Remarkable strides in the theory and application of this toolset over the past three decades, combined with a similarly impressive acceleration in computing capabilities, have helped proliferate the use of optimization software in science, engineering, business, and beyond. Yet, the commercial optimization solvers being utilized in practice often lack rigorous numerical guarantees which, largely unbeknownst to users, may cause them to return inconsistent results. Such outcomes can lead practitioners to draw incorrect conclusions about the problem or system being analyzed and ultimately lead to misguided and erroneous decisions. The rather unpredictable and non-negligible plausibility of these and other incorrect outcomes, which can be traced to the compounding and deleterious effects of roundoff errors, detracts from the implicit trust placed on optimization solvers, and it is specially concerning as these cyberinfrastructures are being widely employed on ever larger and more numerically complex problems. This Faculty Early Career Development (CAREER) project will seek to establish the next generation of optimization solvers with robust numerical guarantees by integrating and building on a mature suite of algorithms for avoiding roundoff errors at low computational cost. The envisioned contributions will result in reliable, open-source optimization solvers that will be made available to academics, practitioners, and the public at large. In addition, the project will design and launch a recruitment and multi-tiered summer research internship program to increase underrepresented student engagement, build critical skills for succeeding in graduate study, and foster interdisciplinary learning communities.This CAREER research project will develop rigorous theory and computational methods to enable the reliable, fail-proof solution of real-world linear programs and mixed integer programs, which is a pivotal guarantee beyond the reach of optimization solvers that work exclusively with finite-precision floating-point arithmetic. To that end, the planned activities will include transforming various inefficient subroutines based on exact rational arithmetic required to validate and/or repair optimization solver outputs, which remain the primary computational bottleneck of mixed-precision optimization solvers with numerical guarantees. The research activities will build on a suite of integer-preserving matrix factorization algorithms, which are primed to be integrated into these state-of-the-art solvers. In addition, the project will explore how to repurpose previous exact primal optimal solutions and exact dual feasible solutions to further enhance the capabilities of mixed-precision optimization solvers with numerical guarantees on numerically challenging problems. The associated activities will include deriving sparse matrix factorization updates, leveraging them to build novel local search methods, and implementing the resulting algorithms on open-source solvers. It is expected that the envisioned theoretical contributions will also have fundamental implications beyond the development of optimization software.This CAREER award is jointly funded by the Software and Hardware Foundations (SHF) Program of the Division of Computing and Communication Foundations (CCF) in the Computer and Information Science and Engineering (CISE) Directorate and the Operations Engineering (OE) Program of the Division of Civil, Mechanical and Manufacturing Innovation (CMMI) in the Engineering (ENG) Directorate.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

数学编程是一种系统的解决问题的方法，它利用数学模型和算法来做出最佳决策，但要受到一组限制。在过去的三十年中，该工具集的理论和应用方面取得了显着的进展，再加上计算能力的同样令人印象深刻的加速度，有助于扩大优化软件在科学，工程，业务以及其他方面的使用。但是，实际上使用的商业优化求解器通常缺乏严格的数值保证，这在很大程度上对用户不知所措，可能会导致他们返回不一致的结果。这些结果可能会导致从业人员得出关于正在分析的问题或系统的错误结论，并最终导致误导和错误的决定。这些和其他不正确结果的相当不可预测和不可忽略的合理性可以追溯到圆形错误的更加复杂和有害的影响，损害了对优化溶解师的隐含信任的损害，并且由于这些Cyber​​infrastures在更大的问题上以及更大的数字问题而变得更加易于使用。这个教师的早期职业发展（职业）项目将寻求建立下一代优化求解器，并通过在成熟的算法套件上集成和构建，以避免以低计算成本避免循环错误，从而以强大的数值保证。设想的贡献将导致可靠的开源优化求解器，并将提供给学者，从业者和整个公众。 In addition, the project will design and launch a recruitment and multi-tiered summer research internship program to increase underrepresented student engagement, build critical skills for succeeding in graduate study, and foster interdisciplinary learning communities.This CAREER research project will develop rigorous theory and computational methods to enable the reliable, fail-proof solution of real-world linear programs and mixed integer programs, which is a pivotal guarantee beyond the reach of optimization solvers that work专门具有有限精确的浮点算术。为此，计划的活动将包括基于验证和/或维修优化的求解器输出所需的确切合理算术转换各种效率低下的子例程，这仍然是具有数值保证的混合精液优化求解器的主要计算瓶颈。研究活动将建立在一组具有整数的基质分解算法的基础上，这些算法被启动为将其集成到这些最新的求解器中。此外，该项目将探索如何重新利用先前的确切原始最佳解决方案和确切的双重可行解决方案，以进一步增强混合精液优化求解器的能力，并在数值上具有挑战性问题的数值保证。相关的活动将包括得出稀疏的矩阵分解更新，利用它们来构建新颖的本地搜索方法以及在开源求解器上实现所得算法。 It is expected that the envisioned theoretical contributions will also have fundamental implications beyond the development of optimization software.This CAREER award is jointly funded by the Software and Hardware Foundations (SHF) Program of the Division of Computing and Communication Foundations (CCF) in the Computer and Information Science and Engineering (CISE) Directorate and the Operations Engineering (OE) Program of the Division of Civil, Mechanical and Manufacturing Innovation (CMMI) in the Engineering (ENG)该奖项反映了NSF的法定任务，并通过使用基金会的知识分子优点和更广泛的影响审查标准来评估值得支持。