Clustering-based preconditioning for stochastic programs

Yankai Cao, Carl D. Laird, Victor M. Zavala
2015 Computational optimization and applications  
We present interior-point strategies for convex stochastic programs in which inexpensive inexact Newton steps are computed from compressed Karush-Kuhn-Tucker (KKT) systems obtained by clustering block scenarios. Using Schur analysis, we show that the compression can be characterized as a parametric perturbation of the full-space KKT matrix. This property enables the possibility of retaining superlinear convergence without requiring matrix convergence. In addition, it enables an explicit
more » ... rization of the residual and we use this characterization to derive a clustering strategy. We demonstrate that high compression rates of 50-90% are possible and we also show that effective preconditioners can be obtained.
doi:10.1007/s10589-015-9813-x fatcat:wkv5wkb2bnb23mues3xteycbze