  In this paper, we propose a modified nonlinear conjugate gradient (NCG)
method for functions with a non-Lipschitz continuous gradient. First, we
present a new formula for the conjugate coefficient \beta_k in NCG, conducting
a search direction that provides an adequate function decrease. We can derive
that our NCG algorithm guarantees strongly convergent for continuous
differential functions without Lipschitz continuous gradient. Second, we
present a simple interpolation approach that could automatically achieve
shrinkage, generating a step length satisfying the standard Wolfe conditions in
each step. Our framework considerably broadens the applicability of NCG and
preserves the superior numerical performance of the PRP-type methods.
