On stochastic and risk averse optimization in networks under incomplete information
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In this talk, we discuss optimization-based approaches to network and graph theoretical problems that arise in situations when the network data is uncertain, incomplete, or conflicting. We employ the stochastic programming framework as well as the formalism of modern risk theory to formulate nontrivial generalizations of several classes of fundamental graph-theoretical problems, such as the maximum weighted clique problem. Several applications of the proposed approach, including identification of minimum-risk structures in randomized networks, determining the “systemic” risk of a distributed networked system, are discussed and illustrated with a number of computational studies. BIO: Pavlo Krokhmal is a Professor in the Systems and Industrial Engineering Department at the University of Arizona. His research interests include decision making and optimization under uncertainty, stochastic programming, risk-averse optimization and risk management, financial engineering, and computational and applied mathematics. He received his Ph.D. in Operations Research from the University of Florida in 2003 and Ph.D. in Mechanics of Solids and Applied Mathematics from Kyiv National Taras Shevchenko University in Ukraine in 1999. He is a recipient of the AFOSR Young Investigator Award and NRC Senior Associateship Award. His research has been supported by the AFOSR, AFRL, DTRA, NSF, and private industry. He is Co-Editor-in-Chief of Optimization Letters, and an Associate Editor of IISE Transactions, Journal of Global Optimization, and SN Operations Research Forum.