A class of nonmonotone trust region algorithms for constrained optimizations

In this note, we consider the following constrained optimization problem (COP) min f(x), x∈Ωwhere f(x): R^n→R is a continuously differentiable function on a closed convex set Ω. Forthe constrained optimization problem (COP), a class of nonmonotone trust region algorithmsis proposed in sec. 1. In sec. 2, the global convergence of this class of algorithms isproved. In sec. 3, some results about the Cauchy point are provided. The

In this note, we consider the following constrained optimization problem (COP) [GRAPHICS] where f(x):R''--> R is a continuously differentiable function on a closed convex set Omega. For the constrained optimization problem (COP), a class of nonmonotone trust region algorithms is proposed in sec. 1. In sec. 2, the global convergence of this class of algorithms is proved. In sec. 3, some results about the Cauchy point are provided. The nonmonotone technique in this algorithm differs from those in existing nonmonotone algorithms, i.e. nonmonotone algorithms with linear search for unconstrained and constrained optimizations([1-5]), and the nonmonotone trust region algorithm for unconstrained optimization([6]). The following notations will be used in this note, f(k)=f(x(k)), g(k)=del f(x(k)), g*=del f(x*), etc. The norm parallel to.parallel to denotes the Euclidean norm in R''.