WARP: A Benchmark for Primal-Dual Warm-Starting of Interior-Point Solvers
For researchers and practitioners in power systems optimization, this work corrects a flawed evaluation baseline and demonstrates the necessity of dual variable prediction for warm-starting interior-point methods.
The paper shows that prior primal-only warm-start methods for AC-OPF do not reduce IPOPT iterations when compared to the solver's actual default initialization, and that only full primal-dual-barrier state prediction can achieve significant iteration reductions (85% in oracle experiments). The authors release a benchmark suite and propose WARP, a graph neural network that predicts the full interior-point state and achieves a 76% reduction in IPOPT iterations.
Solving AC Optimal Power Flow (AC-OPF) is of central importance in electricity market operations, where interior-point methods (IPMs) such as IPOPT are the standard solvers. A growing body of work uses machine learning to predict primal warm-start iterates, reporting iteration reductions of 30-46\%. We show that these reported gains rest on an inappropriate evaluation baseline: prior methods benchmark against the flat start $V_m = 1, V_a = 0$, whereas the solver's actual default - the variable-bound midpoint $(l+u)/2$ - is near-optimal for log-barrier centrality. Against this corrected baseline, no primal-only warm-start method reduces solver iterations. We trace the failure to a geometric property of interior-point methods: primal prediction accuracy is anticorrelated with convergence speed, and providing the ground-truth optimal solution $x^*$ without dual variables causes the solver to diverge. Oracle experiments establish that the complete primal-dual-barrier state $(x^*, λ^*, z^*, μ^*)$ reduces IPOPT iterations from 23 to 3 - an 85\% reduction that is structurally inaccessible to primal-only methods. To enable rigorous evaluation of warm-start methods on this task, we release a benchmark suite comprising dual-labeled AC-OPF datasets with IPOPT-extracted solutions, a corrected evaluation protocol, and WARP - a topology-conditioned encode-process-decode interaction network that predicts the full interior-point state $(\hat{x}, \hatλ, \hat{z}, \hatμ)$ on the heterogeneous constraint graph. WARP achieves a 76\% reduction in IPOPT iterations while natively accommodating N-1 contingency topology variations without retraining.