Open AccessA New Method for Solving Second-Order Cone Eigenvalue Complementarity Problems
Author(s) -
Samir Adly,
Hadia Rammal
Publication year - 2014
Publication title -
journal of optimization theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.109
H-Index - 91
eISSN - 1573-2878
pISSN - 0022-3239
DOI - 10.1007/s10957-014-0645-0
Subject(s) - mathematics , complementarity theory , eigenvalues and eigenvectors , mixed complementarity problem , complementarity (molecular biology) , mathematical optimization , theory of computation , regularization (linguistics) , mathematical analysis , algorithm , computer science , nonlinear system , biology , quantum mechanics , physics , artificial intelligence , genetics
International audienceIn this paper, we study numerical methods for solving eigenvalue complementarity problems involving the product of second-order cones (or Lorentz cones). We reformulate such problem to find the roots of a semismooth function. An extension of the Lattice Projection Method (LPM) to solve the second-order cone eigenvalue complementarity problem is proposed. The LPM is compared to the semismooth Newton methods, associated to the Fischer–Burmeister and the natural residual functions. The performance profiles highlight the efficiency of the LPM. A globalization of these methods, based on the smoothing and regularization approaches, are discussed
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