A pseudo basic step, solved by Lagrangian decomposition, gives provable lower bounds on the improvement from a basic step in convex disjunctive programming, and on K-means instances it closes far more of the optimality gap than commercial solvers.
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Pseudo basic steps: Bound improvement guarantees from Lagrangian decomposition in convex disjunctive programming
A pseudo basic step, solved by Lagrangian decomposition, gives provable lower bounds on the improvement from a basic step in convex disjunctive programming, and on K-means instances it closes far more of the optimality gap than commercial solvers.