An Interior Point Parameterized Central Path Following Algorithm for Linearly Constrained Convex Programming

An Interior Point Parameterized Central Path Following Algorithm for Linearly Constrained Convex Programming

An interior point algorithm is proposed for linearly constrained convex programming following a parameterized central path, which is a generalization of the central path and requires weaker convergence conditions. The convergence and polynomial-time complexity of the proposed algorithm are proved un...

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Bibliographic Details
Main Authors: Hou, L., Qian, X., Liao, L.Z., Sun, Jie
Format: Journal Article
Language:English
Published: SPRINGER/PLENUM PUBLISHERS 2022
Subjects:
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Interior point method
Path following
Polynomial-time complexity
Convex programming
POTENTIAL REDUCTION ALGORITHM
SCALING CONTINUOUS TRAJECTORIES
PREDICTOR-CORRECTOR ALGORITHM
CONTINUATION-SMOOTHING METHOD
POLYNOMIAL-TIME ALGORITHM
PRIMAL-DUAL ALGORITHMS
LIMITING BEHAVIOR
CONVERGENCE
COMPLEXITY
Online Access:http://purl.org/au-research/grants/arc/DP160102918
http://hdl.handle.net/20.500.11937/91422
Description
Summary:An interior point algorithm is proposed for linearly constrained convex programming following a parameterized central path, which is a generalization of the central path and requires weaker convergence conditions. The convergence and polynomial-time complexity of the proposed algorithm are proved under the assumption that the Hessian of the objective function is locally Lipschitz continuous. In addition, an initialization strategy is proposed and some numerical results are provided to show the efficiency and attractiveness of the proposed algorithm.

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