Name
Title | ||
|---|---|---|
On the complexity of finding first-order critical points in constrained nonlinear optimization. |
Abstract | ||
|---|---|---|
The complexity of finding \(\epsilon \)-approximate first-order critical points for the general smooth constrained optimization problem is shown to be no worse that \(O(\epsilon ^{-2})\) in terms of function and constraints evaluations. This result is obtained by analyzing the worst-case behaviour of a first-order short-step homotopy algorithm consisting of a feasibility phase followed by an optimization phase, and requires minimal assumptions on the objective function. Since a bound of the same order is known to be valid for the unconstrained case, this leads to the conclusion that the presence of possibly nonlinear/nonconvex inequality/equality constraints is irrelevant for this bound to apply. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1007/s10107-012-0617-9 | Math. Program. |
Keywords | Field | DocType |
algorithms,minimization | Homotopy algorithm,Discrete mathematics,Mathematical optimization,Nonlinear system,First order,Nonlinear programming,Minification,Critical point (mathematics),Constrained optimization problem,Mathematics,Constrained optimization | Journal |
Volume | Issue | ISSN |
144 | 1-2 | 1436-4646 |
Citations | PageRank | References |
9 | 0.61 | 10 |
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 |