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We consider a general mixed-integer convex program. We first develop analgorithm for solving this problem, and show its finite convergence. We thendevelop a finitely convergent decomposition algorithm that separates binaryvariables from integer and continuous variables. The integer and continuousvariables are treated as second stage variables. An oracle for generating aparametric cut under a subgradient decomposition assumption is developed. Thedecomposition algorithm is applied to show that two-stage (distributionallyrobust) convex programs with binary variables in the first stage can be solvedto optimality within a cutting plane framework. For simplicity, the paperassumes that certain convex programs generated in the course of the algorithmare solved to optimality.

A Finitely Convergent Cutting Plane, and a Bender's Decomposition  Algorithm for Mixed-Integer Convex and Two-Stage Convex Programs using  Cutting Planes