Recent Advances in Constructing Convex Relaxations for Global Optimization
Abstract: Global optimization problems arise in various engineering applications such as modeling thermodynamic equilibria. In state-of-the-art deterministic methods for global minimization (as implemented in the solvers BARON, ANTIGONE, MAiNGO and EAGO.jl), a problem is solved to ε-optimality in finite time by evaluating upper and lower bounds on the unknown globally optimal value, and then successively refining these bounds. Lower bounds here are typically computed by constructing and minimizing an appropriate convex relaxation. Intuitively, for these lower bounds to be useful in global optimization, the supplied convex relaxations must be accurate and tight and they must be constructed both automatically and cheaply. This presentation summarizes established approaches for generating useful convex relaxations of well-behaved functions, and introduces our recent advances in handling implicit functions and solutions of parametric ordinary differential equations, incorporating derivative-free analysis techniques and making effective use of gradient/subgradient information.
Bio: Kamil Khan is an associate professor of Chemical Engineering at McMaster University in Canada. Kamil received his B.S.E. from Princeton University and his Ph.D. from Massachusetts Institute of Technology, both in chemical engineering. He was a Director’s Postdoctoral Fellow in the Mathematics and Computer Science division of the Argonne National Laboratory. His doctoral work was awarded the American Institute of Chemical Engineers’ W. David Smith, Jr. Graduate Student Paper Award.
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