Abstract: We propose to solve Pareto eigenvalue complementarity problems by using interior-point methods. Precisely, we focus the study on an adaptation of the Mehrotra Predictor Corrector Method (MPCM) and a Non-Parametric Interior Point Method (NPIPM). We compare these two methods with two alternative methods, namely the Lattice Projection Method (LPM) and the Soft Max Method (SM). On a set of data generated from the Matrix Market, the performance profiles highlight the efficiency of MPCM and NPIPM for solving eigenvalue complementarity problems. We also consider an application to a concrete and large size situation corresponding to a geomechanical fracture problem. Finally, we discuss the extension of MPCM and NPIPM methods to solve quadratic pencil eigenvalue problems under conic constraints (joint work with Samir Adly and Le Mans Hung.)

References [1] S. ADLY, A. SEEGER, A nonsmooth algorithm for cone-constrained eigenvalue problems, (2011). [2] A. PINTO DA COSTA, A. SEEGER, Cone-constrained eigenvalue problems: theory and algorithms, (2008). [3] A. SEEGER, J. VICENTE-PE ́REZ, On cardinality of Pareto spectra, (2011). [4] D.T.S. VU, I. BEN GHARBIA, M. HADDOU, Q. H. TRAN, A new approach for solving nonlinear algebraic systems with complementarity conditions. Application to compositional multiphase equilibrium problems, (2021).

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