Analysis of some interior point continuous trajectories for convex programming

Abstract

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.

Keywords:

• Continuous trajectory
• interior point method
• convex programming
• ordinary differential equation

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of L.-Z. Liao was supported in part by Hong Kong Baptist University [grant number FRG2/14-15/009], [grant number FRG2/15-16/058] and General Research Fund of Hong Kong [grant number GRF 12319816]. The work of J. Sun was supported in part by Australia Research Council [grant number DP-160102918].