1. Exploiting cone approximations in an augmented Lagrangian method for conic optimization
- Author
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Fukuda, Mituhiro, Gómez, Walter, Haeser, Gabriel, and Makoto, Leonardo M.
- Subjects
Mathematics - Optimization and Control ,90C30, 49M37, 90C26 - Abstract
We propose an algorithm for general nonlinear conic programming which does not require the knowledge of the full cone, but rather a simpler, more tractable, approximation of it. We prove that the algorithm satisfies a strong global convergence property in the sense that it generates a strong sequential optimality condition. In particular, a KKT point is necessarily found when a limit point satisfies Robinson's condition. We conduct numerical experiments minimizing nonlinear functions subject to a copositive cone constraint. In order to do this, we consider a well known polyhedral approximation of this cone by means of refining the polyhedral constraints after each augmented Lagrangian iteration. We show that our strategy outperforms the standard approach of considering a close polyhedral approximation of the full copositive cone in every iteration., Comment: 13 pages, 5 figures
- Published
- 2024