Date/Time
Date(s) - 18/11/2024
9:30 am - 10:30 am

Location: Hamilton Hall, Room 207

Speaker: Kamil Khan (McMaster University)

Title: 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 ?-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 ODEs, incorporating derivative-free analysis techniques, and making effective use of gradient/subgradient information.