A Modified Penalty Function Method for Inequality Constraints Minimization

In this paper we introduce a modified penalty function (MPF) method for solving a problem which minimizes a nonlinear programming subject to inequality constraints. Basically, this method is a combination of the modified penalty methods and the Lagrangian methods. It treats inequality constraints with a modified penalty function and avoids the indifferentiability of max {x, 0}. This method alternatively minimizes the MPF and updates the Lagrange multipliers. It converges linearly for a large enough penalty parameter under the standard second-order optimality conditions and superlinear convergence can be attained by increasing the penalty parameter after updating Lagrange multiplier step by step. Numerical experiments show that the proposed method is considerably faster than the method based on classical penalty function.