This paper presents a new warmstarting technique in the context of a primal-dual column generation method applied to solve a particular class of combinatorial optimization problems. The technique relies on calculating an initial point and on solving auxiliary linear optimization problems to determine the step direction needed to fully restore primal and dual feasibilities after … Read more
One of the main drawbacks associated with Interior Point Methods (IPM) is the perceived lack of an efficient warmstarting scheme which would enable the use of information from a previous solution of a similar problem. Recently there has been renewed interest in the subject. A common problem with warmstarting for IPM is that an advanced … Read more
In this paper, we investigate the use of an exact primal-dual penalty approach within the framework of an interior-point method for nonconvex nonlinear programming. This approach provides regularization and relaxation, which can aid in solving ill-behaved problems and in warmstarting the algorithm. We present details of our implementation within the LOQO algorithm and provide extensive … Read more
One perceived deficiency of interior-point methods in comparison to active set methods is their inability to efficiently re-optimize by solving closely related problems after a warmstart. In this paper, we investigate the use of a primal-dual penalty approach to overcome this problem. We prove exactness and convergence and show encouraging numerical results on a set … Read more