The trust-region subproblem minimizes a general quadratic function over an ellipsoid and can be solved in polynomial time using a semidefinite-programming (SDP) relaxation. Intersecting the feasible set with a second ellipsoid results in the two-trust-region subproblem (TTRS). Even though TTRS can also be solved in polynomial-time, existing algorithms doâ€¦ (More)

This paper studies an extended trust region subproblem (eTRS) in which the trust region intersects the unit ball with m linear inequality constraints. When m = 0, m = 1, or m = 2 and the linear constraints are parallel, it is known that the eTRS optimal value equals the optimal value of a particular convex relaxation, which is solvable in polynomial time.â€¦ (More)

Let F be a quadratically constrained, possibly nonconvex, bounded set, and let E1, . . . , El denote ellipsoids contained in F with non-intersecting interiors. We prove that minimizing an arbitrary quadratic q(Â·) over G := F\âˆªk=1 int(Ek) is no more difficult than minimizing q(Â·) over F in the following sense: if a given semidefinite-programming (SDP)â€¦ (More)

In this paper, we give a new Hardy-Hilbertâ€™s integral inequality with some parameters and a best constant factor. It includes an overwhelming majority of results of many papers.

Cut-generating functions (CGFs) have been studied since 1970s in the context of Mixed Integer Linear Programs (MILPs) and more general disjunctive programs and have drawn renewed attention recently. The sufficiency of CGFs to generate all valid inequalities for the convex hull description of disjunctive sets or all cuts that separate the origin from theâ€¦ (More)

Motivated by the management of sales representatives who visit customers to develop customer relationships, we present a stochastic orienteering problem on a network of queues, in which a hard time window is associated with each customer and the representative may experience uncertain wait time resulting from a queueing process at the customer. In general,â€¦ (More)