For a stochastic programming problem with a nonsmooth objective a recursive stochastic subgradient method is proposed in which successive directions are obtained from quadratic programming subproblems. The subproblems result from linearization of original constraints and from approximation of the objective by a quadratic function involving stochastic epsilon -subgradient estimates constructed in the course of computation. A special Lyapunov function technique is used to show that the method is convergent with probability 1 to stationary points and recovers the subgradient and Lagrange multipliers that appear in necessary conditions of optimality.
All Science Journal Classification (ASJC) codes
- General Mathematics
- Computer Science Applications
- Management Science and Operations Research