Related papers: Guaranteed $\epsilon$-optimal solutions with the l…
Given a set of $m$ points and a set of $n$ lines in the plane, we consider the problem of computing the faces of the arrangement of the lines that contain at least one point. In this paper, we present an $O(m^{2/3}n^{2/3}+(n+m)\log n)$ time…
The dose delivered to the planning target volume by proton beams is highly conformal, sparing organs at risk and normal tissues. New treatment planning systems adapted to spot scanning techniques have been recently proposed to…
This work studies and develop projection-free algorithms for online learning with linear optimization oracles (a.k.a. Frank-Wolfe) for handling the constraint set. More precisely, this work (i) provides an improved (optimized) variant of an…
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…
The numerical properties of algorithms for finding the intersection of sets depend to some extent on the regularity of the sets, but even more importantly on the regularity of the intersection. The alternating projection algorithm of von…
Radiation Therapy (RT) plays a pivotal role in the treatment of cancer, offering the potential to effectively target and eliminate tumour cells while minimizing harm to surrounding healthy tissues. However, the success of RT heavily depends…
Constrained Reinforcement Learning (RL) aims to maximize the return while adhering to predefined constraint limits, which represent domain-specific safety requirements. In continuous control settings, where learning agents govern system…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
The study of online algorithms with machine-learned predictions has gained considerable prominence in recent years. One of the common objectives in the design and analysis of such algorithms is to attain (Pareto) optimal tradeoffs between…
In the past decades mathematical optimization has found its way into radiation therapy and has made profound practice changing impact. Today, virtually all advanced treatment delivery methods, such as IMRT, VMAT, tomotherapy, LDR/HDR…
This paper studies the equitable and optimal transport (EOT) problem, which has many applications such as fair division problems and optimal transport with multiple agents etc. In the discrete distributions case, the EOT problem can be…
In this note we propose a new approach towards solving numerically optimal stopping problems via reinforced regression based Monte Carlo algorithms. The main idea of the method is to reinforce standard linear regression algorithms in each…
We develop a fixed-point iterative algorithm that computes the matrix projection with respect to the Bures distance on the set of positive definite matrices that are invariant under some symmetry. We prove that the fixed-point iteration…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
Intelligent robots provide a new insight into efficiency improvement in industrial and service scenarios to replace human labor. However, these scenarios include dense and dynamic obstacles that make motion planning of robots challenging.…
3D computer-assisted corrective osteotomy has become the state-of-the-art for surgical treatment of complex bone deformities. Despite available technologies, the automatic generation of clinically acceptable, ready-to-use preoperative…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
A framework for online robust adaptive radiation therapy (ART) is presented. This framework is designed to (i) handle interfractional geometric variations following a probability distribution different from the a priori hypothesis, (ii)…
We consider the problem of planning with participation constraints introduced in [Zhang et al., 2022]. In this problem, a principal chooses actions in a Markov decision process, resulting in separate utilities for the principal and the…