Article ID: | iaor1998922 |
Country: | Netherlands |
Volume: | 76 |
Issue: | 3 |
Start Page Number: | 353 |
End Page Number: | 372 |
Publication Date: | Mar 1997 |
Journal: | Mathematical Programming |
Authors: | Ermoliev Y.M., Kryazhimskii Arkadii V., Ruszczyski Andrzej |
Keywords: | gradient methods |
A general constraint aggregation technique is proposed for convex optimization problems. At each iteration a set of convex inequalities and linear equations is replaced by a single surrogate inequality formed as a linear combination of the original constraints. After solving the simplified subproblem, new aggregation coefficients are calculated and the iteration continues. This general aggregation principle is incorporated into a number of specific algorithms. Convergence of the new methods is proved and speed of convergence analyzed. Next, dual interpretation of the method is provided and application to decomposable problems is discussed. Finally, a numerical illustration is given.