Title: Generalized Trust Region Subproblem

The interval bounded generalized trust region subproblem (GTRS)
consists in minimizing a general quadratic objective subject to an
upper and lower bounded general quadratic constraint. In this talk, we
first look at optimality conditions and the relationship between the
problem and its SDP relaxation. We classify this problem into easy
case and hard case instances as for trust region subproblems (TRS),
and demonstrate that the general problem is reducible to an equality
constrained problem after identifying suitable generalized eigenvalues
and possibly solving a sparse system. Finally, we extend the
Rendl-Wolkowicz algorithm for TRS to solve the equality constrained
problem, highlighting its connection with the problem of finding the
minimum generalized eigenvalues of a parameterized matrix pencil.

This is a joint work with Henry Wolkowicz.