A Globally Convergent Method of Constrained Minimization by Solving Subproblems of the Conic Model

A new method for nonlinearly constrained optimization problems is proposed. The method consists of two steps. In the first step, we get a search direction by the linearly constrained subproblems based on conic functions. In the second step, we use a differentiable penalty function, and regard it as the metric function of the problem. From this, a new approximate solution is obtained. The global convergence of the given method is also proved.