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Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. It was shown in Burer (2009) that mixed-binary quadratic programs can be written as completely positive programs, which are convex. Completely positive reformulations of discrete optimization problems therefore have strong duality if a constraint qualification is satisfied. We apply this perspective in two ways. First, we write unit commitment in power systems as a completely positive program, and use the dual copositive program to design a new pricing mechanism. Second, we reformulate integer programming games in terms of completely positive programming, and use the KKT conditions to solve for pure strategy Nash equilibria. To facilitate implementation, we also design a cutting plane algorithm for solving copositive programs exactly.

This work was done in collaboration with Merve Bodur (U. Toronto) and Joshua A. Taylor (U. Toronto).

Bio: Cheng Guo is an Assistant Professor in Operations Research (School of Mathematical and Statistical Sciences) at Clemson University. She received her Ph.D. in Industrial Engineering from University of Toronto in 2021, her M.S. in Operations Research from Columbia University, and her B.A. in Economics and B.S. in Mathematics from Wuhan University, China. Her research interests are in the intersection of optimization and economics, with a focus on energy markets, integer/stochastic programming modeling, and decomposition methods.