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- Daniel Bienstock, Alexander Michalka
- SIAM Journal on Optimization
- 2014

We derive linear inequality characterizations for sets of the form conv{(x, q) ∈ R×R : q ≥ Q(x), x ∈ R − int(P )} where Q is convex and differentiable and P ⊂ R. We show that in several cases our characterization leads to polynomial-time separation algorithms that operate in the original space of variables, in particular when Q is a positive-definite… (More)

- Daniel Bienstock, Alexander Michalka
- SODA
- 2014

We consider an optimization problem of the form min xQx+ cx s.t. ‖x− μh‖ ≤ rh, h ∈ S, ‖x− μh‖ ≥ rh, h ∈ K, x ∈ P, where P ⊆ R is a polyhedron defined by m inequalities and Q is general and the μh ∈ R and the rh quantities are given; a strongly NP-hard problem. In the case |S| = 1, |K| = 0 and m = 0 one obtains the classical trust-region subproblem which is… (More)

Preliminaries. Several important classes of optimization problems include nonlinearities in the objective or constraints. Often this results in nonconvexities and a current research thrust addresses the computation of global bounds and exact solution techniques for such problems. The field is not new; one of the earliest results is the characterization of… (More)

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