Name
Title | ||
|---|---|---|
On the Evaluation Complexity of Cubic Regularization Methods for Potentially Rank-Deficient Nonlinear Least-Squares Problems and Its Relevance to Constrained Nonlinear Optimization. |
Abstract | ||
|---|---|---|
We propose a new termination criterion suitable for potentially singular, zero or nonzero residual, least-squares problems, with which cubic regularization variants take at most O(epsilon(-3/2)) residual- and Jacobian-evaluations to drive either the Euclidean norm of the residual or its gradient below epsilon; this is the best known bound for potentially rank-deficient nonlinear least-squares problems. We then apply the new optimality measure and cubic regularization steps to a family of least-squares merit functions in the context of a target-following algorithm for nonlinear equality-constrained problems; this approach yields the first evaluation complexity bound of order epsilon(-3/2) for nonconvexly constrained problems when higher accuracy is required for primal feasibility than for dual first-order criticality. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1137/120869687 | SIAM JOURNAL ON OPTIMIZATION |
Keywords | Field | DocType |
evaluation complexity,worst-case analysis,least-squares problems,constrained nonlinear optimization,cubic regularization methods | Trust region,Residual,Discrete mathematics,Mathematical optimization,Nonlinear system,Nonlinear programming,Euclidean distance,Regularization (mathematics),Non-linear least squares,Mathematics,Penalty method | Journal |
Volume | Issue | ISSN |
23 | 3 | 1052-6234 |
Citations | PageRank | References |
8 | 0.63 | 12 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Coralia Cartis | 1 | 451 | 28.74 |
| Nicholas I. M. Gould | 2 | 1445 | 123.86 |
| Philippe L. Toint | 3 | 1397 | 127.90 |