Marianna Nagy

A polynomial path-following interior point algorithm for general linear complementarity problems

Linear Complementarity Problems (LCPs) belong to the class of

Symmetry in RLT-type relaxations for the quadratic assignment and standard quadratic optimization problems

{\mathbb{NP}}

On the complexity of computing the handicap of a sufficient matrix

-complete problems. Therefore we cannot expect a polynomial time solution method for LCPs without requiring some special property of the coefficient matrix. Our aim is to construct interior point algorithms which, according to the duality theorem in EP (Existentially Polynomial-time) form, in polynomial time either give a solution of the original problem or detects the lack of property

EP Theorem for Dual Linear Complementarity Problems

{\mathcal{P}_*(\tilde\kappa)}

Forbidden minor characterizations for low-rank optimal solutions to semidefinite programs over the elliptope

, with arbitrary large, but apriori fixed