ISyE Seminar Series: Miguel Lejeune
"Distributionally Robust Maximization of Ratio Exceedance Probability"
Miguel Lejeune
Professor of Decision Sciences and Electrical and Computer Engineering at the George Washington University (GWU)
About the Seminar:
We explore a comprehensive class of distributionally robust optimization models that maximize the probability of exceedance d fined as a ratio of stochastic functions. We develop a general reformulation framework that encompasses two forms of ambiguity (moment and Wasserstein), two types of distributional support (uncertain probabil ties and continuum of realizations), and mu tiple functional forms for the probability of exceedance successively expressed as a ratio of linear-to-linear, linear-to-quadratic, quadratic-to-linear, quadratic-to-quadratic, and linear-to-quadratic norm functions. For each case, we first construct the hypographical formulation taking the form of a semi-infinite optimization problem with a distributionally robust chance constraint in which the probability level is a random variable, and derive then a finite-dimensional and computationally tractable reformulation. For the continuum of realizations support, the reformulations are biconvex problems for which we design a customized algorithm that converges finitely and is general enough to handle all (integer and continuous) biconvex reformulations. The numerical experiments demonstrate the computational efficiency of the proposed reformulations and solution method, and the benefits of adopting a distributionally robust approach for the Sharpe Ratio probability of exceedance.
Joint work with Hoang Nam Nguyen (George Washington University)
About the Speaker:
Miguel Lejeune is a Full Professor of Decision Sciences and Electrical and Computer Engineering at the George Washington University (GWU). He held visiting positions at Carnegie Mellon University, Georgetown University, the University of California – Irvine, the Naval Postgraduate School, the University of Maryland, Paris-Saclay University, in Paris, and the Foundation Getulio Vargas in Rio de Janeiro.
Dr. Lejeune is the recipient of the 2019 Koopman Award of the INFORMS Society, the 2024 Excellence Research Award in Applied Mathematics from the Washington Academy of Science, CAREER/Young Investigator Research Grant from the Army Research Office, and the IBM Smarter Planet Faculty Innovation Award. He received the 2022 Best Paper Award from the Journal of Global Optimization. Dr. Lejeune is a Fellow of the Washington Academy of Science and was an elected board committee member of the Stochastic Programming Society.
Dr. Lejeune’s areas of expertise/research interests include stochastic programming, distributionally robust optimization, and mixed-integer nonlinear programming. His application areas include energy and power systems, health care, financial risk, supply chain management, disaster management, and military operations. His research is currently funded by several grants from the National Science Foundation, the Office of Naval Research, and the DUKE Energy Innovation Fund.
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