An augmented Lagrangian method with second-order update is developed, and its relationship to the sequential quadratic programming method is described. The rate of convergence proof depends on a second-order sufficient optimality condition, which is shown to be satisfied for a class of nonlinear optimal control problems of tracking type. Numerical examples are included which demonstrate the glo...

A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the εk-global minimization of the Augmented Lagrangian with simple constraints, where εk → ε. Global convergence to an ε-global minimizer of the original problem is proved. The subproblems are solved...

In this paper we study optimal control problems of the uid ow governed by the Navier-Stokes equations. Two control problems are formulated in the case of the driven cavity and ow through a channel with sudden expansion and solved successfully using a numerical method based on the augmented Lagrangian method. Existence and rst order optimality condition of the optimal control are established. A ...

Abstract A reformulation of cardinality-constrained optimization problems into continuous nonlinear with an orthogonality-type constraint has gained some popularity during the last few years. Due to special structure constraints, violates many standard assumptions and therefore is often solved using specialized algorithms. In contrast this, we investigate viability a safeguarded multiplier pena...

This paper proposes a Trust-Region Based Augmented Method (TRALM) to solve a combined Environmental and Economic Power Dispatch (EEPD) problem. The EEPD problem is a multi-objective problem with competing and non-commensurable objectives. The TRALM produces a set of non-dominated Pareto optimal solutions for the problem. Fuzzy set theory is employed to extract a compromise non-dominated sol...