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• We consider the constrained stochastic convex optimization by projected subgradient algorithm. • A new convergence analysis approach is developed to prove the validity of the proposed algorithm. • Convergence rate is given without specifying the gains. This paper discusses a kind of convex optimization problem considering noises from information transmission in multi-agent systems. Different from previous works, we focus on the objective function which is a summation of strictly L 0 (F) -convex functions under random inner space. Our system is described by Itô formula, which leads to that it is hard to calculate second-order derivative when designing the projected subgradient algorithm. It is shown that all states in stochastic system will converge to the unique optimal state in the polyhedric set constraint by adopting projected subgradient algorithm and the convergence rate is also investigated. Numerical examples are provided to demonstrate the results. [ABSTRACT FROM AUTHOR]