Constraint aggregation principle in convex optimization

Constraint aggregation principle in convex optimization

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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: , ,
Keywords: gradient methods
Abstract:

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.

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