Structured convex optimization with applications

结构化凸优化及其应用

• 批准号: RGPIN-2019-07199
• 负责人: zinchenko, yuriy
• 金额: $ 1.24万
• 依托单位: University of Calgary
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759198
• 关键词: Structured; convex; optimization; applications

The proposal is a response to a large demand on analytics, and optimization in particular, in Canada, and specifically in Alberta. It supports a goal to establish Calgary as a strong-hold in optimization by building an active industrial mathematics lab. The optimization lab is envisioned as a focal point, producing top quality research and a constant stream of employable HQP. Encompassing (1) applications, (2) theory and (3) numerical algorithms, optimization is ubiquitous to science and engineering. We pursue all three intertwined directions, but above all are motivated by the applications. (1) Applications: our central application area is radiation therapy (RT) in cancer treatment, where optimization plays a key role. In 2007 cancer surpassed cardiovascular disease as the leading cause of death. It is estimated that 2 out of 5 Canadians will develop cancer during their lifetimes; 1 out of 4 will die from cancer. In turn, over 50% of cancer patients are treated with RT. Thus, improving the RT efficacy is an important concern. Due to the large problem size -setting 1,000s of parameters controlling radiation exposure- modern RT planning is very challenging. Optimization methods are used to derive better treatment plans that deliver lethal dose to the tumor surrounded by healthy tissues to be spared. A main challenge in RT planning is incorporation of dose-volume requirements (DVR). DVR ensure the target coverage and survivability of healthy structures. Due their complexity, conventional models to include DVR are computationally intractable. Sadly, an over decade-old call to "optimization experts . (to) improve our ability to solve these difficult problems" in prime applied math journal (Shepard et al, SIAM Review 41(4), 721-744, 1999) is still open today. A recently discovered interplay between the dose moments and the DVR paves an innovative alternative route to solving this problem. A preliminary investigation shows that the approach offers an opportunity to optimize RT plans under DVR in near-real time. We aim to capitalize on this discovery and further investigate the above methods, targeting the development of a new RT optimization framework. In turn, this opens a road to a novel technology in RT, benefiting Canadians and cancer patients world-wide. (2,3) Theory and Algorithms: motivated by the above, we focus on structured convex optimization. Despite recent dramatic advances in optimization theory and computational capacities, we still fall short of solving many challenging real world problems such as RT planning. Better theory and implementations are desperately needed. To improve the theory, we probe into provable limits of IPM-family of most efficient optimization methods known to-date. On the implementation side, we target the development of modular IPM solver to enrich the class of problems that can be solved and enable computational enhancements offered by advanced IT such as GP-GPU.

该提案是对加拿大，特别是阿尔伯塔省对分析，特别是优化的大量需求的回应。它支持通过建立一个活跃的工业数学实验室来建立卡尔加里作为优化的一个强有力的支撑的目标。优化实验室被设想为一个焦点，产生高质量的研究和可雇用的HQP源源不断。包括（1）应用，（2）理论和（3）数值算法，优化是无处不在的科学和工程。我们追求这三个相互交织的方向，但最重要的是受到应用的激励。(1)应用：我们的主要应用领域是癌症治疗中的放射治疗（RT），其中优化起着关键作用。2007年，癌症超过心血管疾病成为死亡的主要原因。据估计，五分之二的加拿大人在其一生中会患上癌症;四分之一的人会死于癌症。反过来，超过50%的癌症患者接受RT治疗。因此，提高RT疗效是一个重要问题。 由于问题规模大-设置1,000个控制辐射暴露的参数-现代RT计划非常具有挑战性。优化方法用于获得更好的治疗计划，将致死剂量传递到被健康组织包围的肿瘤中。RT规划的一个主要挑战是纳入剂量体积要求（DVR）。DVR保证了目标的覆盖和健康结构的生存能力。由于其复杂性，包括DVR的传统模型在计算上是难以处理的。可悲的是，一个十多年前的电话“优化专家。(to)Improving our ability to solve these difficult problems”（谢泼德et al，SIAM Review 41（4），721-744，1999），至今仍在公开。最近发现的剂量时刻和DVR之间的相互作用为解决这个问题铺平了一条创新的替代路线。初步调查表明，该方法提供了一个机会，优化RT计划下DVR在近实时。我们的目标是利用这一发现，并进一步研究上述方法，目标是开发一个新的RT优化框架。反过来，这为RT的新技术开辟了一条道路，使加拿大人和世界各地的癌症患者受益。 （2，3）理论与算法：基于上述动机，本文主要研究结构凸优化问题。尽管最近在优化理论和计算能力方面取得了巨大的进步，但我们仍然无法解决许多具有挑战性的真实的世界问题，如RT规划。迫切需要更好的理论和实施。为了完善这一理论，我们探讨了IPM族最有效的优化方法的可证明极限。在实施方面，我们的目标是开发模块化IPM求解器，以丰富可解决的问题类别，并实现GP-GPU等先进IT提供的计算增强功能。