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Solving Convex Discrete Optimization via Simulation via Stochastic Localization Algorithms Many decision-making problems in operations research and management science require the optimization of large-scale complex stochastic systems. For a number of applications, the objective function exhibits convexity in the discrete decision variables or the problem can be transformed into a convex one. In “Stochastic Localization Methods for Convex Discrete Optimization via Simulation,” Zhang, Zheng, and Lavaei propose provably efficient simulation-optimization algorithms for general large-scale convex discrete optimization via simulation problems. By utilizing the convex structure and the idea of localization and cutting-plane methods, the developed stochastic localization algorithms demonstrate a polynomial dependence on the dimension and scale of the decision space. In addition, the simulation cost is upper bounded by a value that is independent of the objective function. The stochastic localization methods also exhibit a superior numerical performance compared with existing algorithms. 

Abstract To ensure privacy protection and alleviate computational burden, we propose a fast subsmaling procedure for the Cox model with massive survival datasets from multi-centered, decentralized sources. The proposed estimator is computed based on optimal subsampling probabilities that we derived and enables transmission of subsample-based summary level statistics between different storage sites with only one round of communication. For inference, the asymptotic properties of the proposed estimator were rigorously established. An extensive simulation study demonstrated that the proposed approach is effective. The methodology was applied to analyze a large dataset from the U.S. airlines.