CAREER: Large-Scale Optimization Problems with Applications in Emerging Radiotherapy Modalities

放射治疗是最常见的癌症治疗形式之一，在美国每年有近100万患者接受放射治疗。这是一种个性化医疗的形式：从治疗光束的方向和调制到治疗计划，总共有数千个参数，使用称为数值优化的计算方法为每个患者量身定制。一些最近的技术，数学和生物学的见解已经激励了从传统形式的治疗出发，这些包括时空分割治疗;质子治疗;组合光子，质子和电子治疗;和电弧治疗。然而，用这些新的治疗方法设计最佳的个性化治疗也提出了新的数学挑战。该学院的早期职业发展（CAREER）奖资助研究数值优化方法的设计和数学分析，除了在科学和工程中的其他应用外，还将使新的放射治疗方式得到严格的评估和更广泛的使用。该项目的重点是开发和分析大规模确定性和随机优化问题的数值方法。该方案的主要研究目标是：（1）为大规模随机约束优化问题开发有效的抽样算法;（2）为大规模凸锥优化问题开发数值方法，在这些问题中，即使一个牛顿步也太昂贵了。该提案的数学和应用部分都被整合到PI开发的本科生和研究生课程的计算和建模部分中。该拨款还支持PI最近与艺术家和设计师建立的外展合作，旨在扩大公众对当前应用数学研究的欣赏和理解，特别是数学优化在医学，卫生保健，该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准。

Radiotherapy is one of the most common forms of cancer treatment, given to nearly one million patients each year in the United States. It is a form of personalized medicine: everything from the orientation and modulation of the treatment beams to the treatment schedule, altogether, thousands of parameters, are tailored for each patient, using computational methods referred to as numerical optimization. Several recent technological, mathematical, and biological insights have motivated the departure from conventional forms of treatment; these include spatiotemporally fractionated therapy; proton therapy; combined photon, proton, and electron therapy; and arc therapy. However, the design of optimal personalized treatments with these new treatment approaches also present new mathematical challenges. This Faculty Early Career Development (CAREER) award funds research into the design and mathematical analysis of numerical optimization methods which, besides other applications in science and engineering, will enable the rigorous assessment and more widespread use of novel radiotherapy treatment modalities.The focus of the project is the development and analysis of numerical methods for large-scale deterministic and stochastic optimization problems. The primary research objectives of this proposal are (1) to develop efficient sampling algorithms for large-scale stochastic constrained optimization, and (2) to develop numerical methods for large-scale convex conic optimization problems in which even a single Newton-step is too expensive. Both the mathematical and the applied components of the proposal are being integrated into the computational and modeling components of undergraduate and graduate courses developed by the PI. The grant also supports the PI's recently established outreach collaboration with artists and designers, which is aimed at broadening the public's appreciation and understanding of current applied mathematics research, in particular the importance of mathematical optimization in medicine, health care, and beyond.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.