2015/12/23 by Maziar Salahi, Salahi, Maziar, Akram Taati +3
Chemistry · Computer Science · Engineering · Mathematics · #65F15 #90C26 #90C30 #90C46 #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Metal-Organic Frameworks: Synthesis and Applications #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1512.07628
openalex publication_date 2015/12/23 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We study large scale extended trust region subproblems (eTRS) i.e., the\nminimization of a general quadratic function subject to a norm constraint,\nknown as the trust region subproblem (TRS) but with an additional linear\ninequality constraint. It is well known that strong duality holds for the TRS\nand that there are efficient algorithms for solving large scale TRS problems.\nIt is also known that there can exist at most one local non-global minimizer\n(LNGM) for TRS. We combine this with known characterizations for strong duality\nfor eTRS and, in particular, connect this with the so-called hard case for TRS.\n We begin with a recent characterization of the minimum for the TRS via a\ngeneralized eigenvalue problem and extend this result to the LNGM. We then use\nthis to derive an efficient algorithm that finds the global minimum for eTRS by\nsolving at most three generalized eigenvalue problems.\n