An iteration process with a known feasible point

(jz) #1

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!


Conjugate transpose should be used,