A stochastic approximation method for convex programming with many semidefinite constraints

In this paper, we consider a type of semidefinite programming problem (MSDP), which involves many (not necessarily finite) of semidefinite constraints. MSDP can be established in a wide range of applications, including covering ellipsoids problem and truss topology design. We propose a random method based on a stochastic approximation technique for solving MSDP, without calculating and storing the multiplier. Under mild conditions, we establish the almost sure convergence and expected convergence rates of the proposed method. A variety of simulation experiments are carried out to support our theoretical results.