A line-search method for Lagrangian relaxation ascent algorithms
Zhao Gong Yun and Zhuangwei Liu
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 often
encountered in solving the dual problem by using some ascent method,
such as bundle methods, interior point method, 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 relaxed subproblem, and therefore are
time-consuming. In this short report we will propose an efficient 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 evaluation of the dual function.
Technical Report No. 644, Department of Mathematics, National University
of Singapore, 0511, SINGAPORE
Contact: Zhuangwei Liu ([email protected]), Zhao Gong Yun ([email protected])