2020/04/17 by Roland Herzog, Herzog, Roland, Eric Legler +1
Computer Science · Decision Sciences · Mathematics · #Advanced Multi-Objective Optimization Algorithms #Advanced Optimization Algorithms Research #Computer science #Economics #FOS: Mathematics #Mathematical economics #Mathematical optimization #Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Order (exchange) #Probabilistic and Robust Engineering Design #cs.NA #math.NA #math.OC
paper · pdf · doi:10.48550/arxiv.2004.08084
published in arXiv (Cornell University) (Cornell University)
arxiv created 2020/04/17 · openalex publication_date 2020/04/17 · arxiv updated 2020/04/20 · openalex created_date 2020/04/24 · openalex updated_date 2026/07/28
We consider a class of convex optimization problems over the simplex of probability measures. Our framework comprises optimal experimental design (OED) problems, in which the measure over the design space indicates which experiments are being selected. Due to the presence of additional bound constraints, the measure possesses a Lebesgue density and the problem can be cast as an optimization problem over the space of essentially bounded functions. For this class of problems, we consider two first-order methods including FISTA and a proximal extrapolated gradient method, along with suitable stopping criteria. Finally, acceleration strategies targeting the dimension of the subproblems in each iteration are discussed. Numerical experiments accompany the analysis throughout the paper.