Interior point methods for solving cone-constrained eigenvalue problems

In this paper, we propose to solve cone-constrained eigenvalue problems by using interiorpoint 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 the Lattice Projection Method (LPM) and the SoftMax Method (SM). The performance profiles, on a set of data generated from the MatrixMarket, 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.