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In engineering design, an optimized solution often turns out to be suboptimal, when errors are encountered. While the theory of robust convex optimization has taken significant strides over the past decade, all approaches fail if the underlying cost function is not explicitly given; it is even worse if the cost function is nonconvex. In this work, we(More)
W e propose a new robust optimization method for problems with objective functions that may be computed via numerical simulations and incorporate constraints that need to be feasible under perturbations. The proposed method iteratively moves along descent directions for the robust problem with nonconvex constraints and terminates at a robust local minimum.(More)
In engineering design, the physical properties of a system can often only be described by numerical simulation. Optimization of such systems is usually accomplished heuristically without taking into account that there are implementation errors that lead to very suboptimal, and often, infeasible solutions. We present a robust optimization method for(More)
Cancer treatment with ionizing radiation is often compromised by organ motion, in particular for lung cases. Motion uncertainties can significantly degrade an otherwise optimized treatment plan. We present a spatiotemporal optimization method, which takes into account all phases of breathing via the corresponding 4D-CTs and provides a 4D-optimal plan that(More)
Intensity-Modulated Radiation Therapy (IMRT) is the technique of delivering radiation to cancer patients by using non-uniform radiation fields from select angles, with the aims of reducing the intensity of the beams that go through critical structures and reaching the dose prescription in the target volume. Two decisions are of fundamental importance: to(More)
Complex systems can be optimized to improve the performance with respect to desired functionalities. An optimized solution, however, can become suboptimal or even infeasible, when errors in implementation or input data are encountered. We report on a robust simulated annealing algorithm that does not require any knowledge of the problems structure. This is(More)
Optimized chirped mirrors may perform suboptimally, or completely fail to satisfy specifications, when manufacturing errors are encountered. We present a robust optimization method for designing these dispersion-compensating mirror systems that are used in ultrashort pulse lasers. Possible implementation errors in layer thickness are taken into account(More)
A novel robust optimization algorithm is demonstrated that is largely deterministic, and yet it attempts to account for statistical variations in coating. Through Monte Carlo simulations of manufacturing, we compare the performance of a proof-of-concept antireflection (AR) coating designed with our robust optimization to that of a conventionally optimized(More)
In engineering design, an optimized solution often turns out to be suboptimal, when implementation errors are encountered. While the theory of robust convex optimization has taken significant strides over the past decade, all approaches fail if the underlying cost function is not explicitly given; it is even worse if the cost function is nonconvex. In this(More)
The purpose was to study correlations amongst IMRT DVH evaluation points and how their relaxation impacts the overall plan. 100 head-and-neck cancer cases, using the Eclipse treatment planning system with the same protocol, are statistically analyzed for PTV, brainstem, and spinal cord. To measure variations amongst the plans, we use (i) interquartile range(More)