Inexact reduced gradient methods in nonconvex optimization

Understand

This paper proposes and develops new linesearch methods with inexact gradient information for finding stationary points of nonconvex continuously differentiable functions on finite-dimensional spaces.

• Some abstract convergence results for a broad class of linesearch methods are stablished.
• A general scheme for inexact reduced gradient (IRG) methods is proposed, where the errors in the gradient approximation automatically adapt with the magnitudes of the exact gradients.
• The sequences of iterations are shown to obtain stationary accumulation points when different stepsize selections are employed.