An active-set algorithm for norm constrained quadratic problems

We present an algorithm for the minimization of a nonconvex quadratic function subject to linear inequality constraints and two-sided bound on 2-norm its solution. The minimizes objective using active-set method by solving series Trust-Region Subproblems (TRS). Underpinning efficiency this approach is that global solution TRS has been widely studied in literature, resulting remarkably efficient algorithms software. extend these results proving nonglobal minimizers TRS, or certificate their absence, can also be calculated efficiently computing two rightmost eigenpairs eigenproblem. demonstrate usefulness scalability experiments often outperform state-of-the-art approaches; include calculation high-quality search directions arising Sequential Quadratic Programming problems CUTEst collection, Sparse Principal Component Analysis large text corpus problem (70 million nonzeros) help organize documents user interpretable way.