A Relaxed Interior Point Method for Low-Rank Semidefinite Programming Problems with Applications to Matrix Completion
A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal solution, a special nearly low-rank form of all primal itera...
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| Veröffentlicht in: | Journal of scientific computing 2021-11, Vol.89 (2), p.46-46, Article 46 |
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| creator | Bellavia, Stefania Gondzio, Jacek Porcelli, Margherita |
| description | A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal solution, a special nearly low-rank form of all primal iterates is imposed. To accommodate such a (restrictive) structure, the first order optimality conditions have to be relaxed and are therefore approximated by solving an auxiliary least-squares problem. The relaxed interior point framework opens numerous possibilities how primal and dual approximated Newton directions can be computed. In particular, it admits the application of both the first- and the second-order methods in this context. The convergence of the method is established. A prototype implementation is discussed and encouraging preliminary computational results are reported for solving the SDP-reformulation of matrix-completion problems. |
| doi_str_mv | 10.1007/s10915-021-01654-1 |
| format | Article |
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| subjects | Algorithms Approximation Computational Mathematics and Numerical Analysis Convergence Efficiency Least squares method Linear algebra Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Matrices (mathematics) Methods Optimization Semidefinite programming Theoretical |
| title | A Relaxed Interior Point Method for Low-Rank Semidefinite Programming Problems with Applications to Matrix Completion |
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