What is it about?
In this paper, we show for the first time superlinear convergence behavior of an implementable interior point algorithm on an important class of matrix optimization problems, linear semi-definite feasibility problems, using search directions found in existing interior point solvers.
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Why is it important?
This is the first time that superlinear convergence behavior of an implementable interior point algorithm on linear semi-definite feasibility problems using search directions found in existing interior point solvers is proved. The key to show this is to apply the algorithm on the homogeneous feasibility model of the given problem. This model is implemented in some existing interior point solvers.
Perspectives
The paper is part of a series of work on the study of superlinear convergence of interior point algorithms on semi-definite programs, and it reveals that working on the right model when solving an optimization problem plays an important role in how well the problem can be solved.
Dr Chee Khian Sim
University of Portsmouth
Read the Original
This page is a summary of: Superlinear convergence of an interior point algorithm on linear semi-definite feasibility problems, Optimization Methods and Software, September 2024, Taylor & Francis,
DOI: 10.1080/10556788.2024.2400705.
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