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Prof. Boris Mordukhovich Department of Mathematics and Institute for AI and Data Science Wayne State University, Detroit, Michigan USA Application of Optimization to Proton Therapy The talk is devoted to investigating single-objective and multiobjective optimization problems involving the so-called l0-norm function, which is nondifferentiable and nonconvex. Such problems appear in proton beam therapy models of cancer research. The developed approach uses first-order and second-order subdifferential tools of variational analysis and scalarization techniques of multiobjective optimization. Based on this machinery, we propose several algorithms of the subgradient and generalized Newtonian types and conduct their convergence analysis. The obtained results are illustrated by numerical examples from proton therapy models. (Based on the collaboration with the Proton Therapy Center of the Corewell William Beaumont Hospital, Royal Oak, Michigan.) |
