How to solve constraint qualification failure

1. Jul 11, 2011

tanzl

I am currently solving a problem (similar to optimal control theory) involving optimization of an integral with mixed and pure constraints. eg: $\int F(x,u,t) dt$ subject to x(t)$\geq$0 , u(t)$\geq$0.

The problem can be solved by Pontryagin minimum principle by introducing the Hamiltonian function and Langragian function and its corresponding necessary conditions. Solving the necessary conditions will yield optimal solutions for different cases.

However, the necessary conditions require the constraint qualification (CQ) to hold, ie: CQ matrix to be full rank. I have problem with some cases which they violate CQ (not full rank). Can anyone please suggest some techniques to solve the problem. Thanks.