  In this paper, we study a new generalization of the Lorentz cone, called the
Monotone Extended Second Order Cone (MESOC). We investigate basic properties of
MESOC including computation of its Lyapunov rank and proving its reducibility.
Moreover, we show that in an ambient space, a cylinder is an isotonic
projection set with respect to MESOC. We also examine a Nonlinear
Complementarity Problem on a cylinder, which is equivalent to a suitable Mixed
Complementarity Problem and provide a computational example illustrating
applicability of MESOC.
