Rank Constraint |

A semidefinite feasibility problem is a convex optimization problem, over a subset of the positive semidefinite cone, having no objective function. Constraining rank of a feasible solution can be thought of as introducing a linear objective function whose normal opposes the direction of search. If one knows the proper search direction, then a solution of desired rank can be found. " In Chapter 4.4, we show how to determine what linear objective function will replace a rank constraint in a semidefinite program. Finding the normal representing that linear function turns out to be a convex optimization problem over a Fantope. Fantopes are introduced in Chapter 2. Some semidefinite problems having a rank constraint can thereby be formulated as convex optimization problems. |