Equilibrium bias and convergence in augmented primal--dual dynamics with sampled constraints
This work studies the stability and convergence of augmented primal-dual dynamics when constraint values are estimated from samples. Unbiased constraint observations can produce a biased augmented multiplier signal, shifting the equilibria of the mean dynamics. For componentwise inequalities, we give a necessary and sufficient condition for preserving the Karush-Kuhn-Tucker (KKT) equilibria and construct a convex example with a locally exponentially stable equilibrium that violates complementarity. To address this bias, constraint values are estimated recursively before forming the augmented multiplier signal. For smooth convex conic problems, a joint energy analysis establishes boundedne...
| Authors | Kang Liu, Mengxiao Chen, Siqi Xiong et al. |
|---|---|
| Primary category | math.OC |
| Published | 12 September 2026 |
| Last updated at source | 12 September 2026 |
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