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On complementary eigenvalue problem

Докладчик: A. Iusem, Instituto de Matematika Pura e Aplicada (IMPA), Rio de Janeiro  RJ, Brazil

Резюме. We introduce the Complementary Eigenvalue Problem (EiCP), and present basic results on existence and number of solutions. We discuss next som ии  e state-of-the-art methods for its solution; namely the spectral gradient method for the symmetric case and the hybrid method (combining a semismooth Newton method with a branch and boundsearch procedure) for the nonsymmetric case. Then we consider three extensions of the problem: The Conic Complementary Eigenvalue Problem (CEiCP), the Quadratic Complementary Eigenvalue Problem (QEiCP) and the Quadratic Conic Complementary Eigenvalue Problem (QCEiCP). We present some existence results for these problems, and describe a procedure which reduces a QEiCP to a higher dimensional EiCP (or a QCEiCP to CEiCP), so that these extensions can be efficiently solved with suitable adaptations of the above mentioned numerical methods for EiCP.

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