SOME RESULTS ON CONSTANT RANK CONSTRAINT QUALIFICATIONS FOR SECOND-ORDER CONE PROGRAMMING IN TWO-DIMENSIONAL SPACE

Tóm tắt

The well-known constant rank constraint qualification introduced by Janin for nonlinear programming has been recently extended to a conic context by exploiting the eigenvector structure of the problem. In this paper, we study the constant rank constraint qualification for second-order cone programming in a special case. Specifically, in twodimensional space, we prove that the constant rank constraint qualification for second-order cone programming coincides with the facial constant rank property. Furthermore, it reduces to the constant rank constraint qualification for nonlinear programming.