A Line Search Method In Lagrangian Relaxation Algorithms

The Lagrangian relaxation strategy (or dualization) is one of the most important methodologies of optimization for solving structured large-scale mathematical programming problems. The line search procedure is very often encountered in solving the dual problem by using some ascent algorithm, such as a bundle algorithm, or an interior point algorithm, etc.. The existing line search methods, for example, Armijo's method, need to evaluate the dual objective function many times, in which each evaluation of the dual objective is to solve a relaxation subproblem. Therefore they are time-consuming. In this paper we will propose an eecient line search method which is applicable to the Lagrangian relaxation ascent algorithms. The advantage of the new method is that the line search is embedded in the evaluation of the dual objective function. Abbreviated Title: Line search method.