Name
Abstract | ||
|---|---|---|
We consider equality-constrained optimization problems, where a given solution may not satisfy any constraint qualification but satisfies the standard second-order sufficient condition for optimality. Based on local identification of the rank of the constraints degeneracy via the singular-value decomposition, we derive a modified primal-dual optimality system whose solution is locally unique, nondegenerate, and thus can be found by standard Newton-type techniques. Using identification of active constraints, we further extend our approach to mixed equality- and inequality-constrained problems, and to mathematical programs with complementarity constraints (MPCC). In particular, for MPCC we obtain a local algorithm with quadratic convergence under the second-order sufficient condition only, without any constraint qualifications, not even the special MPCC constraint qualifications. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1137/S1052623403427264 | SIAM Journal on Optimization |
Keywords | Field | DocType |
constraint qualification,constraints degeneracy,special mpcc constraint qualification,local identification,second-order sufficient condition,newton-type methods,local algorithm,mathematical programs with complementarity constraints mpcc,newton method,modified primal-dual optimality system,constraint qualifications,standard newton-type technique,complementarity constraint,second-order sufficiency,optimization problems,active constraint,regularity,singular-value decom- position,optimization problem,singular value decomposition,satisfiability,quadratic convergence,singular value,second order | Complementarity (molecular biology),Singular value decomposition,Mathematical optimization,Constraint (mathematics),Degeneracy (mathematics),Local algorithm,Rate of convergence,Optimization problem,Mathematics,Newton's method | Journal |
Volume | Issue | ISSN |
15 | 1 | 1052-6234 |
Citations | PageRank | References |
13 | 0.97 | 26 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| A. F. Izmailov | 1 | 238 | 21.76 |
| M. V. Solodov | 2 | 600 | 72.47 |