joint work with Tibor Illés, Janez Povh, Petra Renáta Rigó
We introduce a new predictor-corrector (PC) interior-point algorithm (IPA), which is suitable for solving linear complementarity problem (LCP) with P*(K)-matrices. We use the method of algebraically equivalent transformation (AET) of the nonlinear equation of the system which defines the central path. We show the complexity of this algorithm and implement it in C++ programming language. We demonstrate its performance on two families of LCPs: LCP with matrices, which have positive handicap and on instances of LCP related to the copositivity test.
Multi-type symmetric non-negative matrix factorization problem is a strong model to approach data fusion e.g. in bioinformatics. It can be formulated as a non-convex optimization problem with the objective function being polynomial of degree 6 and the feasible set being defined by sign and complementarity constraints. In the talk we will present how to obtain good solutions, often local extreme points, by the fixed point method, the projected gradient method, the Alternating Direction Method of Multipliers and ADAM. We also demonstrate the application of this approach in cancer research.