 Award ID(s):
 1814840
 Publication Date:
 NSFPAR ID:
 10336403
 Journal Name:
 ACM Transactions on Modeling and Computer Simulation
 Volume:
 31
 Issue:
 4
 Page Range or eLocationID:
 1 to 36
 ISSN:
 10493301
 Sponsoring Org:
 National Science Foundation
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In a chance constrained program (CCP), decision makers seek the best decision whose probability of violating the uncertainty constraints is within the prespecified risk level. As a CCP is often nonconvex and is difficult to solve to optimality, much effort has been devoted to developing convex inner approximations for a CCP, among which the conditional valueatrisk (CVaR) has been known to be the best for more than a decade. This paper studies and generalizes the ALSOX, originally proposed by Ahmed, Luedtke, SOng, and Xie in 2017 , for solving a CCP. We first show that the ALSOX resembles a bilevel optimization, where the upperlevel problem is to find the best objective function value and enforce the feasibility of a CCP for a given decision from the lowerlevel problem, and the lowerlevel problem is to minimize the expectation of constraint violations subject to the upper bound of the objective function value provided by the upperlevel problem. This interpretation motivates us to prove that when uncertain constraints are convex in the decision variables, ALSOX always outperforms the CVaR approximation. We further show (i) sufficient conditions under which ALSOX can recover an optimal solution to a CCP; (ii) an equivalent bilinear programming formulationmore »

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Abstract We consider estimation of the density of a multivariate response, that is not observed directly but only through measurements contaminated by additive error. Our focus is on the realistic sampling case of bivariate panel data (repeated contaminated bivariate measurements on each sample unit) with an unknown error distribution. Several factors can affect the performance of kernel deconvolution density estimators, including the choice of the kernel and the estimation approach of the unknown error distribution. As the choice of the kernel function is critically important, the class of flattop kernels can have advantages over more commonly implemented alternatives. We describe different approaches for density estimation with multivariate panel responses, and investigate their performance through simulation. We examine competing kernel functions and describe a flattop kernel that has not been used in deconvolution problems. Moreover, we study several nonparametric options for estimating the unknown error distribution. Finally, we also provide guidelines to the numerical implementation of kernel deconvolution in higher sampling dimensions.

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