Name
Title | ||
|---|---|---|
Inexact Josephy–Newton framework for generalized equations and its applications to local analysis of Newtonian methods for constrained optimization |
Abstract | ||
|---|---|---|
We propose and analyze a perturbed version of the classical Josephy–Newton method for solving generalized equations. This
perturbed framework is convenient to treat in a unified way standard sequential quadratic programming, its stabilized version,
sequential quadratically constrained quadratic programming, and linearly constrained Lagrangian methods. For the linearly
constrained Lagrangian methods, in particular, we obtain superlinear convergence under the second-order sufficient optimality
condition and the strict Mangasarian–Fromovitz constraint qualification, while previous results in the literature assume (in
addition to second-order sufficiency) the stronger linear independence constraint qualification as well as the strict complementarity
condition. For the sequential quadratically constrained quadratic programming methods, we prove primal-dual superlinear/quadratic
convergence under the same assumptions as above, which also gives a new result. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1007/s10589-009-9265-2 | Computational Optimization and Applications |
Keywords | Field | DocType |
Newton method,Josephy–Newton method,Generalized equation,Variational problem,Linearly constrained Lagrangian method,(Stabilized) sequential quadratic programming | Second-order cone programming,Quadratic growth,Mathematical optimization,Quadratically constrained quadratic program,Mathematical analysis,Rate of convergence,Quadratic programming,Sequential quadratic programming,Mathematics,Constrained optimization,Newton's method | Journal |
Volume | Issue | ISSN |
46 | 2 | 0926-6003 |
Citations | PageRank | References |
12 | 0.86 | 17 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| A. F. Izmailov | 1 | 238 | 21.76 |
| M. V. Solodov | 2 | 600 | 72.47 |