One-level additive overlapping Schwarz keeps CG iterations bounded (≤16) on growing synthetic 2D pose-graph SLAM problems, unlike unpreconditioned CG which grows past 10k iterations.
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On the strong concavity of the dual function of an optimization problem
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abstract
We provide three new proofs of the strong concavity of the dual function of some convex optimization problems. For problems with nonlinear constraints, we show that the the assumption of strong convexity of the objective cannot be weakened to convexity and that the assumption that the gradients of all constraints at the optimal solution are linearly independent cannot be further weakened. Finally, we illustrate our results with several examples.
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2026 1verdicts
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Overlapping Schwarz Preconditioners for Pose-Graph SLAM in Robotics
One-level additive overlapping Schwarz keeps CG iterations bounded (≤16) on growing synthetic 2D pose-graph SLAM problems, unlike unpreconditioned CG which grows past 10k iterations.