  The maximum (or minimum) generalized eigenvalue of symmetric positive
semidefinite matrices that depend on optimization variables often appears as
objective or constraint functions in structural topology optimization when we
consider robustness, vibration, and buckling. It can be an unbounded or
discontinuous function where matrices become singular (where a topological
change of the structural design occurs). Based on variational analysis, we
redefine the maximum (and minimum) generalized eigenvalue function as an
extended real-valued function and propose a real-valued continuous
approximation of it. Then, we show that the proposed approximation
epi-converges to the original redefined function, which justifies solving
problems with the approximation instead. We consider two specific topology
optimization problems: robust compliance optimization and eigenfrequency
optimization and conduct simple numerical experiments.
