| In the field of optimization solutions, the derivative-free methods play an important role, and also have been developed more widely. Nonmonotone derivative-free augmented Lagrangian is the main work in this paper, which is a particular subset of direct search methods that neither compute nor approximate any derivatives, but make use of the function values in the algorithm. In the meanwhile, the nonmonotone technique is also included, in the absence of the decrease of the objective functions, we state the conver-gence of the algorithm.The main job of this paper can be divided into two aspects, which may be summa-rized as follows:1. Chapter 2 discusses the nonmonotone derivative-free augmented Lagrangian algo-rithm for solving equality constrained optimizations. We make use of the framework of the augmented Lagrangian introduced in [7], and make a little progress to some extent. In this paper, we always suppose that both the objective function and the constrained function are twice continuously differentiable on Rn. We demand that the search direc-tions should satisfy some conditions. Moreover, the sufficient stepsize is produced by the nonmonotone derivative-free algorithm, which can guarantee the sufficient reduction of the objectives function values. Finally, we state the global convergence of the algorithm.2. Chapter 3 discusses the nonmonotone derivative-free augmented Lagrangian al-gorithm for solving the nonlinear equality and inequality constrained optimizations. In this paper, our approach is based on the augmented Lagrangian framework given in [2]. It does not need to turn the inequality constraints into equality constraints, but keep the original forms. Making use of the convergent properties obtained from the nonmono-tone derivative-free linesearch algorithm and the augmented Lagrangian algorithm, and according to the constant positive linear dependence condition for the constrained func-tions, we prove the global convergent result of the original problem.
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