A Primal-Dual Exterior Point Method for Nonlinear Optimization

In this paper, a primal dual method for general possible nonconvex nonlinear optimization problems is considered. The method is an exterior point type method which means that it permits primal variables violate inequality constraints during the iterations. The method is based on exact penalty type transformation of inequality constraints, and use smooth approximation of the problem to form primal-dual iteration based on Newton method as in usual primal-dual interior point method. The global convergence and local superlinear/quadratic convergence of the proposed methods are proved. For global convergence, methods using line search and trust region are proposed. The method is tested with CUTE problems, and is shown to have similar efficiency to the primal-dual interior point method proposed by Yamashita, Yabe and Tanabe. It is also shown that the method can enjoy warm start conditions easily unlike interior point methods.

• Type: Journal
• Year: 2010
• Where: SIAMJO
• Authors: Hiroshi Yamashita, Takahito Tanabe
• Keywords: Global Convergence, Inequality Constraints, Interior Point Methods, SIAMJO 2010