A fast eigenvalue approach for solving the trust region subproblem with an additional linear inequality

Journal Article · Thu Mar 15 00:00:00 EDT 2018 · Computational and Applied Mathematics

DOI:https://doi.org/10.1007/S40314-016-0347-3· OSTI ID:22769384

Taati, A. ^[1]

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1. University of Guilan, Faculty of Mathematical Sciences (Iran, Islamic Republic of)

In this paper, we study the extended trust region subproblem (eTRS) in which the trust region intersects the Euclidean ball with a single linear inequality constraint. By reformulating the Lagrangian dual of eTRS as a two-parameter linear eigenvalue problem, we state a necessary and sufficient condition for its strong duality in terms of an optimal solution of a linearly constrained bivariate concave maximization problem. This results in an efficient algorithm for solving eTRS of large size whenever the strong duality is detected. Finally, some numerical experiments are given to show the effectiveness of the proposed method.

• OSTI ID: 22769384
• Journal Information: Computational and Applied Mathematics, Vol. 37, Issue 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); ISSN 0101-8205
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ALGORITHMS
EIGENVALUES
EUCLIDEAN SPACE
LAGRANGIAN FUNCTION
MATHEMATICAL SOLUTIONS
RELAXATION