Advanced Convex Relaxations for Nonconvex Stochastic Programs and AC Optimal Power Flow

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SHAO-DISSERTATION-2020.pdf (1.8 MB)
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Shao, Yuanxun
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School of Chemical and Biomolecular Engineering
School established in 1901 as the School of Chemical Engineering; in 2003, renamed School of Chemical and Biomolecular Engineering
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http://hdl.handle.net/1853/64205
Abstract
Mathematical optimization problems arise in nearly all areas of engineering design, operations, and control. However, optimization models of practical interest are often nonconvex, large-scale, and uncertain. All of these factors severely complicate the solution of these problems and make it much more difficult to locate true global solutions rather than inferior local solutions. The new algorithms developed in this Ph.D. work enable more efficient solutions of nonconvex stochastic optimization problems, stochastic optimal control problems, and AC optimal power flow problems than previously possible. Moreover, this work contributes fundamental advances to global optimization theory that may lead to efficient solutions of larger and more complex optimization problems in other areas as well. Higher quality decision-making in such systems could possibly save energy and provide affordable products to impoverished areas.
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2020-12-06
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