Alexander Michalka The trust region subproblem concerns the minimization of a general quadratic over the unit ball in R^n. Extensions to this problem are of interest because of applications to, for example, combinatorial optimization. However the extension obtained by adding an arbitrary family of linear side constraints is NP-hard. In this paper we consider variants of the … Read more
Motivated by mixed-integer, nonlinear optimization problems, we derive linear inequality characterizations for sets of the form conv{(x, q ) \in R^d × R : q \in Q(x), x \in R^d – int(P )} where Q is convex and differentiable and P \subset R^d . We show that in several cases our characterization leads to polynomial-time … Read more
In this paper we derive strong linear inequalities for sets of the form {(x, q) ∈ R^d × R : q ≥ Q(x), x ∈ R^d − int(P ) }, where Q(x) : R^d → R is a quadratic function, P ⊂ R^d and “int” denotes interior. Of particular but not exclusive interest is the … Read more