Spectral projected subgradient method for nonsmooth convex optimization problems

We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate and variable sample size strategy employed. proposed algorithm combines an SAA subgradient spectral coefficient order provide suitable direction which improves performance first method as shown by numerical results. step sizes are chosen from predefined interval almost sure convergence proved under standard assumptions stochastic environment. To enhance algorithm, we further specify choice introducing Armijo-like procedure adapted this framework. Considering computational cost on machine learning problems, conclude that line search significantly. Numerical experiments conducted finite sum also reveal outperforms full approach.