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Robust optimization is a commonly employed method to mitigate uncertainties in the planning of intensity-modulated proton therapy (IMPT). In certain contexts, the large number of uncertainty scenarios makes the robust problem impractically…

We provide a new perspective on the study of parameterized optimization problems. Our approach combines methods for post-optimal sensitivity analysis and ordinary differential equations to quantify the uncertainty in the minimizer due to…

Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…

We propose a prognostic stratum matching framework that addresses the deficiencies of Randomized trial data subgroup analysis and transforms ObservAtional Data to be used as if they were randomized, thus paving the road for precision…

Optimization is a critical tool for addressing a broad range of human and technical problems. However, the paradox of advanced optimization techniques is that they have maximum utility for problems in which the relationship between the…

Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys…

Spectral imaging is a method in medical x-ray imaging to extract information about the object constituents by the material-specific energy dependence of x-ray attenuation. Contrast-enhanced spectral imaging has been thoroughly investigated,…

Spatiotemporal fractionation schemes, that is, treatments delivering different dose distributions in different fractions, may lower treatment side effects without compromising tumor control. This is achieved by hypofractionating parts of…

In many areas, practitioners seek to use observational data to learn a treatment assignment policy that satisfies application-specific constraints, such as budget, fairness, simplicity, or other functional form constraints. For example,…

Decision analysis deals with modeling and enhancing decision processes. A principal challenge in improving behavior is in obtaining a transparent description of existing behavior in the first place. In this paper, we develop an expressive,…

While the use of combination therapy is increasing in prevalence for cancer treatment, it is often difficult to predict the exact interactions between different treatment forms, and their synergistic/antagonistic effects on patient health…

Cancer remains a leading cause of death worldwide, necessitating personalized treatment approaches to improve outcomes. Theranostics, combining molecular-level imaging with targeted therapy, offers potential for precision oncology but…

The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…

We study the problem of finding an optimal radiotherapy treatment plan. A time-dependent Boltzmann particle transport model is used to model the interaction between radiative particles with tissue. This model allows for the modeling of…

Hyperparameter optimization (HPO) is generally treated as a bi-level optimization problem that involves fitting a (probabilistic) surrogate model to a set of observed hyperparameter responses, e.g. validation loss, and consequently…

We establish a broad methodological foundation for mixed-integer optimization with learned constraints. We propose an end-to-end pipeline for data-driven decision making in which constraints and objectives are directly learned from data…

Purpose: Optical imaging is evolving as a key technique for advanced sensing in the operating room. Recent research has shown that machine learning algorithms can be used to address the inverse problem of converting pixel-wise multispectral…

In this paper, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that contraction is a concept naturally suitable…

Modern external beam cancer radiotherapy applies prescribed radiation doses to tumor targets while minimally affecting nearby vulnerable organs-at-risk (OARs). Creating a treatment plan is difficult and time-consuming with no guarantee of…

The modern workflow for radiation therapy treatment planning involves mathematical optimization to determine optimal treatment machine parameters for each patient case. The optimization problems can be computationally expensive, requiring…