Hi there,

I got a problem when running a series of optimization problems, in which CVX is used to produce a feasible point in each step. It is proved that the series of generated points will converge to a stationary point.

The original constraint is in the form g^+(x)-g^-(x)\leq0 where g^+(x) and g^-(x) are both convex functions.

It is then approximated by \tilde{g}({x};{u}) \triangleq g^+({x}) - g^-({u}) - \bigtriangledown_{{x}} g^-({u})^T({x}-{u}) \le 0, where u is a given feasible point for the original constraint.

When running this part, *sometimes* CVX says the problem is “infeasible”. I’ve double checked the feasibility of u, so apparently the approximated constraint should have at least one feasible point, i.e., u itself.

Could you please give me any idea why CVX couldn’t get the correct answer?..

PS: in my problem g^+(x) and g^-(x) are positive semidefinite quadratic functions of complex vectors, and in my code the only the real part (\bigtriangledown_{{x}} g^-({u})^T({x}-{u})) is taken into account. Maybe this is the reason?

Many thanks in advance!