Minimizing Nonsmooth Convex Functions with Variable Accuracy

We consider unconstrained optimization problems with nonsmooth and convex objective function in the form of mathematical expectation. The proposed method approximates the objective function with a sample average function by using different sample size in each iteration. The sample size is chosen in an adaptive manner based on the Inexact Restoration. The method uses line … Read more

Spectral projected gradient method for stochastic optimization

We consider the Spectral Projected Gradient method for solving constrained optimization problems with the objective function in the form of mathematical expectation. It is assumed that the feasible set is convex, closed and easy to project on. The objective function is approximated by a sequence of Sample Average Approximation functions with different sample sizes. The … Read more

Nonmonotone line search methods with variable sample size

Nonmonotone line search methods for unconstrained minimization with the objective functions in the form of mathematical expectation are considered. The objective function is approximated by the sample average approximation (SAA) with a large sample of fixed size. The nonmonotone line search framework is embedded with a variable sample size strategy such that different sample size … Read more

Line search methods with variable sample size for unconstrained optimization

Minimization of unconstrained objective function in the form of mathematical expectation is considered. Sample Average Approximation – SAA method transforms the expectation objective function into a real-valued deterministic function using large sample and thus deals with deterministic function minimization. The main drawback of this approach is its cost. A large sample of the random variable … Read more