Name
Abstract | ||
|---|---|---|
In this paper we study optimization problems involving eigenvalues of symmetric matrices. One of the difficulties with numerical analysis of such problems is that the eigenvalues, considered as functions of a symmetric matrix, are not differentiable at those points where they coalesce. We present a general framework for a smooth (differentiable) approach to such problems. It is based on the concept of transversality borrowed from differential geometry. In that framework we discuss first- and second-order optimality conditions and rates of convergence of the corresponding second-order algorithms. Finally we present some results on the sensitivity analysis of such problems. |
Year | DOI | Venue |
|---|---|---|
1995 | 10.1137/0805028 | SIAM JOURNAL ON OPTIMIZATION |
Keywords | Field | DocType |
NONSMOOTH OPTIMIZATION,TRANSVERSALITY CONDITION,FIRST-ORDER AND 2ND-ORDER OPTIMALITY CONDITIONS,NEWTONS ALGORITHM,QUADRATIC RATE OF CONVERGENCE,SEMIINFINITE PROGRAMMING,SENSITIVITY ANALYSIS | Mathematical optimization,Semi-infinite programming,Symmetric matrix,Differentiable function,Differential geometry,Transversality,Random optimization,Optimization problem,Eigenvalues and eigenvectors,Mathematics | Journal |
Volume | Issue | ISSN |
5 | 3 | 1052-6234 |
Citations | PageRank | References |
33 | 21.49 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alexander Shapiro | 1 | 1273 | 147.62 |
| Michael K. H. Fan | 2 | 54 | 27.44 |