A general nonlinear complementarity problem (NCP) is formulated as a finite set optimization problem called binary NCP, where design variables are identified by n-bit binary numbers. The binary NCP corresponds to the problem of finding a vertex of an n-dimensional unit cube with zero cost value. Two geometrically intuitive algorithms based on the geometry of the unit cube and another algebraically intuitive one based on the distribution of negative variables are implemented. They are called VSA (vertex search algorithm), FSA (face search algorithm), and NSA (negative-entry search algorithm). FSA and NSA are robust as shown by test problems of small to medium size. FSA, which is like a coordinate search algorithm, is much superior to the other two. It is simple to program and most reliable not only for NCPs but also for a new category called joker search problems.

一般的非线性互补问题（NCP）被公式化为称为二进制NCP的有限集优化问题，其中设计变量由n位二进制数标识。二进制NCP对应于找到n的顶点的问题零成本值的三维单位立方体。实现了两种基于单位立方体几何形状的几何直观算法和另一种基于负变量分布的几何直观算法。它们被称为VSA（顶点搜索算法），FSA（人脸搜索算法）和NSA（负条目搜索算法）。FSA和NSA具有强大的功能，如中小型测试问题所示。FSA就像坐标搜索算法一样，比其他两个要好得多。它不仅易于编程，而且对NCP而言最可靠，而且对于称为“小丑搜索问题”的新类别也最可靠。