LANS Informal Seminar: Kamil Khan

Seminar Title: Differentiable convex underestimators for global optimization
Speaker: Kamil Khan, Postdoc

Date/Time: 2016-07-06 15:00
Location: Bldg 240 rms 1404-1405

Description:
Several deterministic methods for global nonconvex minimization require lower-bounding information that is obtained using convex underestimators of the objective function and constraints. To be useful, these underestimators ought to be computable by a procedure that is cheap, accurate, and automatable, and should converge rapidly to the original function as the considered domain shrinks. Established underestimator generation methods by McCormick (1976) and Tsoukalas and Mitsos (2014) satisfy all of these desired properties, but often produce underestimators that are nonsmooth. Nonsmoothness makes optimization difficult, and can hinder extraction of lower-bounding information from the obtained underestimators. To circumvent these issues, this seminar describes a variant of Tsoukalas and Mitsos’s underestimating scheme that yields once- or twice-continuously differentiable underestimators while preserving all of the useful properties of their approach. A C++ implementation is discussed, along with extensions to nonconvex implicit functions and solutions of parametric ordinary differential equations.