Nonmonotone Trust Region Algorithm For Equality Constrained Optimization

Trust region method is a kind of efficient and robust method to solve general constrained optimization. This thesis combines the nonmonotone technique and proposes a nonmonotone trust region algorithm to solve equality constrained optimization. The nonmonotone degree is controlled by algorithm self-adapt, when we calculate the ratio of predicted reduction and actual reduction, we adopt the information of the frontal m(k) dots. It is differ from previously adopted the information of the frontal a dot when we calculate the ratio of predicted reduction and actual reduction. The merit function is augmented Lagrange function. Trust region subproblem is similar to one in [32].When we solve the trust region subproblem, we equivalently transform it into unconstrained trust region subproblem. We prove that the algorithm is well defined and the global convergence of method is obtained without regular conditions. Preliminary numerical results show the algorithm is effective, and nonmonotone trust region algorithm is more effective than...