On warm starts for interior methods

An appealing feature of interior methods for linear programming is that the number of iterations required to solve a problem tends to be relatively insensitive to the choice of initial point. This feature has the drawback that it is difficult to design interior methods that efficiently utilize information from an optimal solution to a ``nearby'' problem. We discuss this feature in the context of general nonlinear programming and specialize to linear programming. We demonstrate that warm start for a particular nonlinear programming problem, given a near-optimal solution for a ``nearby'' problem, is closely related to an SQP method applied to an equality-constrained problem. These results are further refined for the case of linear programming.


In IFIP International Federation for Information Processing, volume 199, System Modeling and Optimization, eds. F. Ceragioli, A. Dontchev, H. Furuta, K. Marti, and L. Pandolfi, pp. 51-66. Springer, Boston, 2006.