A Reduced Space Branch and Bound Algorithm for Globaloptimization
Journal of Global Optimization
Efficient Global Optimization of Expensive Black-Box Functions
Journal of Global Optimization
An Algorithm for Global Minimization of Linearly Constrained Quadratic Functions
Journal of Global Optimization
Multisection in Interval Branch-and-Bound Methods for Global Optimization – I. Theoretical Results
Journal of Global Optimization
A Taxonomy of Global Optimization Methods Based on Response Surfaces
Journal of Global Optimization
Branch-and-bound approaches to standard quadratic optimization problems
Journal of Global Optimization
Convergence of duality bound method in partly convex programming
Journal of Global Optimization
Optimal Multisections in Interval Branch-and-Bound Methods of Global Optimization
Journal of Global Optimization
On Solving Nonconvex Optimization Problems by Reducing The Duality Gap
Journal of Global Optimization
Decomposition Methods for Solving Nonconvex Quadratic Programs via Branch and Bound*
Journal of Global Optimization
Journal of Global Optimization
Journal of Global Optimization
Journal of Global Optimization
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We view the beam orientation optimization (BOO) problem in intensity-modulated radiation therapy (IMRT) treatment planning as a global optimization problem with expensive objective function evaluations. We propose a response surface method that, in contrast with other approaches, allows for the generation of problem data only for promising beam orientations as the algorithm progresses. This enables the consideration of additional degrees of freedom in the treatment delivery, i.e., many more candidate beam orientations than is possible with existing approaches to BOO. This ability allows us to include noncoplanar beams and consider the question of whether or not noncoplanar beams can provide significant improvement in treatment plan quality. We also show empirically that using our approach, we can generate clinically acceptable treatment plans that require fewer beams than are used in current practice.