The convergence of maximum entropy methods is obtained on Kuhn-Tucker/Fritz John points. Then according to the nature of maximum entropy methods, we study the structure and convergent properties of feasible directions methods with nonmonotone curvilinear search rules from the unified point. On this basis, we discuss the numerically computing technique which combines nonmonotone curvilinear search methods and maximum entropy methods, and the numerically computing results for some optimization problems are obtained. The results show that our algorithm is efficient.