This paper proposes and develops new line search 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 line search methods are reviewed and
extended. A general scheme for inexact reduced gradient (IRG) methods with
different stepsize selections are proposed to construct sequences of iterates
with stationary accumulation points. Convergence results with convergence rates
for the developed IRG methods are established under the Kurdyka-Lojasiewicz
property. The conducted numerical experiments confirm the efficiency of the
proposed algorithms