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Title of the Paper: A Semismooth Inexact Newton-type Method for the Solution
of Optimal Power Flow Problem
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Authors: Xue Li, Yuzeng Li, Shaohua Zhang
Abstract: The paper presents a semismooth inexact Newton-type method for solving optimal power flow (OPF) problem. By introducing the nonlinear complementarity problem (NCP) function, the Karush-Kuhn-Tucker (KKT) conditions of OPF model are transformed equivalently into a set of semismooth nonlinear algebraic equations. Then the set of semismooth equations can be solved by an improved inexact Levenberg-Marquardt (L-M) algorithm based on the subdifferential. In the algorithm, the positive definitiveness of the iterative coefficient matrix is enhanced by using the L-M parameter, while a reformed nonmonotone line search is used to enforce global convergence of the algorithm. Finally, the feasibility of the proposed method for solving the nondifferentiable problem is verified on Kojima-Shindo problem, and the effectiveness of the proposed method is demonstrated on the IEEE test systems.
Keywords: inexact Levenberg-Marquardt algorithm; nonlinear complementarity problem; optimal power flow; power system; subdifferential
Title of the Paper: Bias-Aware Linear Combinations of Variance Estimators
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Authors: Wenchi Chiu, David Goldsman, Wheyming T. Song
Abstract: A prototype problem in the analysis of steady-state stochastic processes is that of estimating the variance
of the sample mean. A commonly used performance criterion for variance estimators is the mean-squared-error
(mse) — the sum of the variance and the squared bias. In this paper, we attempt to minimize the variance of
an estimator subject to a bias constraint — a goal that differs from that of minimizing mse, in which case there
would be no explicit bias constraint. We propose a bias-aware mechanism to achieve our goal. Specifically, we
use linear combinations of estimators based on different batch sizes to approximately satisfy the bias constraint;
and then we minimize the variance by choosing appropriate linear combination weights. We illustrate the use
of this mechanism by presenting bias-aware linear combinations of several variance estimators, including nonoverlapping
batch means, overlapping batch means, and standardized time series weighted area estimators. We
also evaluate our mechanism with Monte Carlo examples.
Keywords: Simulation, Mean-squared-error, Variance Estimation, Non-overlapping Batch Means, Overlapping
Batch Means, Standardized Time Series, Weighted Area Estimator.
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