1. The Monotone Extended Second-Order Cone and Mixed Complementarity Problems
- Author
-
Sandor Nemeth, Yingchao Gao, and Roman Sznajder
- Subjects
Pure mathematics ,Control and Optimization ,Monotone polygon ,Rank (linear algebra) ,Cone (topology) ,Applied Mathematics ,Complementarity (molecular biology) ,Nonlinear complementarity problem ,Management Science and Operations Research ,Mixed complementarity problem ,Projection (linear algebra) ,Ambient space ,Mathematics - Abstract
In this paper, we study a new generalization of the Lorentz cone $$\mathcal{L}^n_+$$ L + n , 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.
- Published
- 2021