作者：Belotti, Pietro; Buchanan, Austin; Ezazipour, Soraya
作者单位：Polytechnic University of Milan; Oklahoma State University System; Oklahoma State University - Stillwater
摘要：In the academic literature and in expert testimony, the Polsby-Popper score is the most popular way to measure the compactness of a political district. Given a district with area A and perimeter P, its Polsby-Popper score is given by (4 pi A)=P2. This score takes values between zero and one, with circular districts achieving a perfect score of one. In this paper, we propose the first mathematical optimization models to draw districts (or districting plans) with optimum Polsby-Popper score. Spe...
作者：Lam, Henry; Zhang, Junhui
作者单位：Columbia University; Columbia University
摘要：We consider stochastic gradient estimation using only black-box function evaluations, where the function argument lies within a probability simplex. This problem is motivated from gradient-descent optimization procedures in multiple applications in distributionally robust analysis and inverse model calibration involving decision variables that are probability distributions. We are especially interested in obtaining gradient estimators where one or few sample observations or simulation runs app...
