Sufficient weighted second-order cone complementarity problems

In this paper, we investigate the properties of a weighted second-order cone complementarity problem (wSOCCP), which covers a wide range of complementarity problems with applications in equilibrium problems from engineering and economics.We show that the column sufficient wSOCCP with cross commutative property has a convex (perhaps empty) solution set.In particular, when the weight vector is zero, the reverse implication is also true.