The Monotone Extended Second-Order Cone and Mixed Complementarity Problems
研究一种新的锥结构——单调扩展二阶锥，分析其基本性质（如Lyapunov秩、可约性），并证明圆柱体是其等距投影集，进而将圆柱上的非线性互补问题转化为混合互补问题，给出计算实例。
Abstract In this paper, we study a new generalization of the Lorentz cone $$\mathcal{L}^n_+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> <mml:mi>n</mml:mi> </mml:msubsup> </mml:math> , 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.