The interval bounded generalized trust region subproblem (GTRS) consists in minimizing a general quadratic objective, q <Subscript>0</Subscript>(x)→min, subject to an upper and lower bounded general quadratic constraint, ℓ≤q <Subscript>1</Subscript>(x)≤u. This means that there are no definiteness assumptions on either quadratic...</subscript></subscript>

The elegant theoretical results for strong duality and strict complementarity for linear programming, LP, lie behind the success of current algorithms. In addition, preprocessing is an essential step for efficiency in both simplex type and interior-point methods. However, the theory and...