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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 explicitdoi:10.1007/s10589-015-9813-x fatcat:wkv5wkb2bnb23mues3xteycbze