Abstract
A random subgradient method is proposed for the general convex feasibility problemwith very large (or infinite) number of inequalities. Under the strong feasibility assumption the method terminates in a finite number of iterations with probability one. A convergent version of the method for infeasible case is also provided. The algorithm can be applied for solving linear matrix inequalities arising in control. Numerical simulation demonstrates high efficiency of the approach for large dimensional problems.
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