Friday, April 10, 2020 - 1:00pm to Saturday, April 11, 2020 - 1:55pm
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This talk addresses “chance-constrained optimization" problems with probabilistic polynomial constraints and also "chance optimization" problems where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective of developing systematic numerical procedures to solve such problems, a sequence of convex relaxations based on the theory of measures and moments and theory of sum of squares polynomials is provided, whose sequence of optimal values are shown to converge to the optimal value of the original problem. Indeed, we provide a sequence of semidefinite programs of increasing dimension which can arbitrarily approximate the solution of the original problem.
Ashkan Jasour is a Research Scientist at the Computer Science and Artificial Intelligence Laboratory (CSAIL) at the Massachusetts Institute of Technology (MIT). In 2016, he received his Ph.D. in Control Systems/Electrical Engineering and a PhD minor in Mathematics from Pennsylvania State University. He also was a Postdoctoral Associate for two years with the Model-based Embedded and Robotic Systems (MERS) group at MIT's CSAIL. His work focuses on developing new rigorous mathematical tools and algorithms to address challenging problems in Control Systems, Robotics, and Optimization. In particular, his research interests include probabilistic control, chance-constrained optimization, stochastic systems, robotic systems, and machine learning.