In this paper, we give an example of a semidefinite programming problem in which primal-dual affine-scaling algorithms using the HRVW/KSH/M, MT, and AHO directions fail. We prove that each of these algorithms can generate a sequence converging to a non-optimal solution and that, for the AHO direction, even its associated continuous trajectory can converge to a non-optimal point. In contrast with these directions, we show that the primal-dual affine-scaling algorithm using the NT direction for the same semidefinite programming problem always generates a sequence converging to the optimal solution. Both primal and dual problems have interior feasible solutions and unique optimal solutions which satisfy strict complementarity, and are nondegenerate everywhere.
|Original language||English (US)|
|Number of pages||27|
|Journal||Mathematics of Operations Research|
|State||Published - 1999|
All Science Journal Classification (ASJC) codes
- Computer Science Applications
- Management Science and Operations Research