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Nonconvex Optimization For Statistical Learning With Structured Sparsity, Chengyu Ke
Nonconvex Optimization For Statistical Learning With Structured Sparsity, Chengyu Ke
Operations Research and Engineering Management Theses and Dissertations
Sparse learning problems, known as feature selection problems or variable selection problems, are a popular branch in the field of statistical learning. When faced with a dataset with only a few observations but a large number of features, we are interested in extracting the most useful features automatically by solving an optimization problem. In this dissertation, we start by introducing a novel penalty function as well as an iterative reweighted algorithm to solve the group sparsity problem, a special type of feature selection problems. The penalty function, named group LOG, shows a better ability to recover the ground-truth compared to …
Study Of Stochastic Market Clearing Problems In Power Systems With High Renewable Integration, Saumya Sakitha Sashrika Ariyarathne
Study Of Stochastic Market Clearing Problems In Power Systems With High Renewable Integration, Saumya Sakitha Sashrika Ariyarathne
Operations Research and Engineering Management Theses and Dissertations
Integrating large-scale renewable energy resources into the power grid poses several operational and economic problems due to their inherently stochastic nature. The lack of predictability of renewable outputs deteriorates the power grid’s reliability. The power system operators have recognized this need to account for uncertainty in making operational decisions and forming electricity pricing. In this regard, this dissertation studies three aspects that aid large-scale renewable integration into power systems. 1. We develop a nonparametric change point-based statistical model to generate scenarios that accurately capture the renewable generation stochastic processes; 2. We design new pricing mechanisms derived from alternative stochastic programming …