A Conic Trust-Region Method for Nonlinearly Constrained Optimization *

Abstract

Trust-region methods are powerful optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. Can we combine their advantages to form a more powerful method for constrained optimization? In this paper we give a positive answer and present a conic trust-region algorithm for non-linearly constrained optimization problems. The trust-region subproblem of our method is to minimize a conic function subject to the linearized constraints and the trust region bound. The use of conic functions allows the model to interpolate function values and gradient values of the Lagrange function at both the current point and previous iterate point. Since conic functions are the extension of quadratic functions, they approximate general nonlinear functions better than quadratic functions. At the same time, the new algorithm possesses robust global properties. In this paper we establish the global convergence of the new algorithm under standard conditions.