Analysis of some interior point continuous trajectories for convex programming. (3rd April 2017)

• Record Type: Journal Article
• Authors: Qian, Xun; Liao, Li-Zhi; Sun, Jie
• Is Part Of: Optimization. Volume 66:Number 4(2017)
• Page Start: 589
• Page End: 608
• Publication Date: 2017-04-03
• Subjects: Continuous trajectory -- interior point method -- convex programming -- ordinary differential equation; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1279160
• Languages: English
• ISSNs: 0233-1934

Abstract

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.