Some Nonmonotone Algorithms For LC～1 And Nonsmooth Minmax Unconstrained Optimization

In this paper, we mainly consider the LC1 unconstrained programming min f(x), where f : Rn → R,f ∈ LC1, that means V/ is a locally Lipschitzian function. In Chapter 2, we present a nonmonotone line search model algorithm for the unconstrained LC1 optimization problems, and prove that our algorithm is globally convergent. And in Chapter 3, we combine the trust region algorithm given by Sun with nonmonotone technique and present a nonmonotone trust region algorithm for the problems and give the global convergence of the algorithm. In Chapter 4, we give a new trust region algorithm with radius bounded below for LC1 unconstrained optimization and prove that it is globally convergent. In Chapter 5, we consider nonsmooth discrete minimax problems minmax{/i(z)|i = 1, ???, m}, where each fi is convex, but not necessarily differentiable. The nonmonotone line search algorithm for nonsmooth optimization given by Pang is extended to this case, and we prove that the algorithm is globally convergent.