The augmented Lagrangian method based on the APG strategy for an inverse damped gyroscopic eigenvalue problem

Yue Lu () and Liwei Zhang ()

Computational Optimization and Applications, 2015, vol. 62, issue 3, 815-850

Abstract: In this paper, we propose an augmented Lagrangian method based on the accelerated proximal gradient (APG) strategy for an inverse damped gyroscopic eigenvalue problem (IDGEP), which is a special case of the classical inverse quadratic eigenvalue problem. Under mild conditions, we show that the whole sequence of iterations generated by the proposed algorithm converges to the unique solution of the IDGEP. In view of the iteration-complexity, the proposed algorithm requires at most $$O(\log (\varepsilon ^{-1}))$$ O ( log ( ε - 1 ) ) outer iterations and at most $$O(\varepsilon ^{-1})$$ O ( ε - 1 ) APG calls to obtain an $$\varepsilon $$ ε -feasible and $$\varepsilon $$ ε -optimal solution of the IDGEP. Numerical results indicate that the proposed algorithm can solve the test problems efficiently. Copyright Springer Science+Business Media New York 2015

Keywords: Inverse damped gyroscopic eigenvalue problem; Augmented Lagrangian method; Accelerated proximal gradient method; Iteration-complexity; 15A18; 65F15; 65F18; 65K05; 90C22; 90C25 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10589-015-9757-1

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