**Abstract**: Optimization models for economic problems with binary decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. For example, in convex markets, shadow (dual) prices are associated with market equilibrium, and for convex games the existence and uniqueness of Nash equilibrium can be proved via fixed-point theorem and KKT conditions. Those results are lacking in their nonconvex counterparts.

We use copositive programming to formulate discrete problems in applications including nonconvex energy markets and nonconvex games, to leverage its convexity and strong duality features. We obtain several novel theoretical and numerical results for those applications, including (1) a new revenue-adequate and individually-rational pricing mechanism for energy markets, and (2) existence, uniqueness, and KKT conditions for the pure-strategy Nash equilibrium in discrete games. We also propose a novel and easy-to-implement cutting-plane algorithm for mixed-integer copositive programs, and employ it in our applications.

**Bio**: Cheng Guo is an Assistant Professor in Operations Research (School of Mathematical & 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 in 2017, and her B.A. in Economics and B.S. in Mathematics from Wuhan University, China in 2015. She also visited Columbia University and worked on the DOE ARPA-E PERFORM project (2021-2022). Her research combines realistic optimization modeling/computation and stylized economic analysis, with focuses on nonconvexity and uncertainty in energy markets, integer and stochastic programming modeling, and decomposition methods.