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View article: Stationary probabilities and the monotone likelihood ratio in bonus-malus systems
Stationary probabilities and the monotone likelihood ratio in bonus-malus systems Open
The bonus-malus system (BMS) is a widely recognized and commonly employed risk management tool. A well-designed BMS can match expected insurance payments with estimated claims even in a diverse group of risks. Although there has been abund…
View article: The smallest mono-unstable, homogeneous convex polyhedron has at least 7 vertices
The smallest mono-unstable, homogeneous convex polyhedron has at least 7 vertices Open
We prove that every homogeneous convex polyhedron with only one unstable equilibrium (known as a mono-unstable convex polyhedron) has at least $7$ vertices. Although it has been long known that no mono-unstable tetrahedra exist, and mono-u…
View article: Spatiotemporal fractionation schemes for stereotactic radiosurgery of multiple brain metastases
Spatiotemporal fractionation schemes for stereotactic radiosurgery of multiple brain metastases Open
Background Stereotactic radiosurgery (SRS) is an established treatment for patients with brain metastases (BMs). However, damage to the healthy brain may limit the tumor dose for patients with multiple lesions. Purpose In this study, we in…
View article: The smallest mono-unstable convex polyhedron with point masses has 8 faces and 11 vertices
The smallest mono-unstable convex polyhedron with point masses has 8 faces and 11 vertices Open
In the study of monostatic polyhedra, initiated by John H. Conway in 1966, the main question is to construct such an object with the minimal number of faces and vertices. By distinguishing between various material distributions and stabili…
View article: A novel stochastic optimization method for handling misalignments of proton and photon doses in combined treatments
A novel stochastic optimization method for handling misalignments of proton and photon doses in combined treatments Open
Objective. Combined proton–photon treatments, where most fractions are delivered with photons and only a few are delivered with protons, may represent a practical approach to optimally use limited proton resources. It has been shown that, …
View article: Technical note: Optimal allocation of limited proton therapy resources using model‐based patient selection
Technical note: Optimal allocation of limited proton therapy resources using model‐based patient selection Open
Purpose We consider the following scenario: A radiotherapy clinic has a limited number of proton therapy slots available each day to treat cancer patients of a given tumor site. The clinic's goal is to minimize the expected number of compl…
View article: Alfonso: Matlab Package for Nonsymmetric Conic Optimization
Alfonso: Matlab Package for Nonsymmetric Conic Optimization Open
We present alfonso, an open-source Matlab package for solving conic optimization problems over nonsymmetric convex cones. The implementation is based on the authors’ corrected analysis of a method of Skajaa and Ye. It enables optimization …
View article: Sum-of-Squares Optimization without Semidefinite Programming
Sum-of-Squares Optimization without Semidefinite Programming Open
We propose a homogeneous primal-dual interior-point method to solve sum-of-squares optimization problems by combining non-symmetric conic optimization techniques and polynomial interpolation. The approach optimizes directly over the sum-of…
View article: PO-0900: Spatiotemporal fractionation schemes for liver stereotactic body radiotherapy
PO-0900: Spatiotemporal fractionation schemes for liver stereotactic body radiotherapy Open
View article: Optimization of spatiotemporally fractionated radiotherapy treatments with bounds on the achievable benefit
Optimization of spatiotemporally fractionated radiotherapy treatments with bounds on the achievable benefit Open
Spatiotemporal fractionation schemes, that is, treatments delivering different dose distributions in different fractions, can potentially lower treatment side effects without compromising tumor control. This can be achieved by hypofraction…
View article: On "A Homogeneous Interior-Point Algorithm for Non-Symmetric Convex Conic Optimization"
On "A Homogeneous Interior-Point Algorithm for Non-Symmetric Convex Conic Optimization" Open
In a recent paper, Skajaa and Ye proposed a homogeneous primal-dual interior-point method for non-symmetric conic optimization. The authors showed that their algorithm converges to $\varepsilon$-accuracy in $O(\sqrtν\log \varepsilon^{-1})$…
View article: Spatiotemporal fractionation schemes for liver stereotactic body radiotherapy
Spatiotemporal fractionation schemes for liver stereotactic body radiotherapy Open
View article: Semi-Infinite Programming using High-Degree Polynomial Interpolants and Semidefinite Programming
Semi-Infinite Programming using High-Degree Polynomial Interpolants and Semidefinite Programming Open
In a common formulation of semi-infinite programs, the infinite constraint set is a requirement that a function parametrized by the decision variables is nonnegative over an interval. If this function is sufficiently closely approximable b…
View article: Scenario generation for stochastic optimization problems via the sparse grid method
Scenario generation for stochastic optimization problems via the sparse grid method Open
View article: Optimization approaches to volumetric modulated arc therapy planning
Optimization approaches to volumetric modulated arc therapy planning Open
Volumetric modulated arc therapy (VMAT) has found widespread clinical application in recent years. A large number of treatment planning studies have evaluated the potential for VMAT for different disease sites based on the currently availa…