Department of Mathematics
Analysis of some interior point continuous trajectories for convex programming
In this paper, we analyse three interior point continuous trajectories for convex programming with general linear constraints. The three continuous trajectories are derived from the primal–dual path-following method, the primal–dual affine scaling method and the central path, respectively. Theoretical properties of the three interior point continuous trajectories are fully studied. The optimality and convergence of all three interior point continuous trajectories are obtained for any interior feasible point under some mild conditions. In particular, with proper choice of some parameters, the convergence for all three interior point continuous trajectories does not require the strict complementarity or the analyticity of the objective function. These results are new in the literature.
Continuous trajectory, convex programming, interior point method, ordinary differential equation
Source Publication Title
Taylor & Francis
This work was supported in part by National Natural Science Foundation of China, under Grant 61273311 and Grant 61173094, in part by the Faculty Research Fund, Hong Kong Baptist University, and in part by the General Research Fund, Hong Kong.
Link to Publisher's Edition
Qian, X., Liao, L., & Sun, J. (2017). Analysis of some interior point continuous trajectories for convex programming. Optimization, 66 (4), 589-608. https://doi.org/10.1080/02331934.2017.1279160