WARP: A Benchmark for Primal-Dual Warm-Starting of Interior-Point Solvers

TL;DR

This paper introduces WARP, a benchmark and neural network model for predicting the full interior-point state in AC-OPF problems, significantly reducing solver iterations and enabling rigorous evaluation of warm-start methods.

Contribution

It corrects evaluation baselines for primal warm-starts, releases a benchmark suite with solutions, and presents WARP, a model predicting primal-dual states to improve solver efficiency.

Findings

Primal-only warm-starts do not reduce iterations against the corrected baseline.

Full primal-dual predictions reduce IPOPT iterations from 23 to 3, an 85% reduction.

WARP achieves 76% reduction in iterations and handles contingency variations without retraining.

Abstract

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 $(x^*, \lambda^*, z^*, \mu^*)$ 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 $(\hat{x}, \hat{\lambda}, \hat{z}, \hat{\mu})$ on the heterogeneous constraint graph. WARP achieves a 76\% reduction in IPOPT iterations while natively accommodating N-1 contingency topology variations without retraining.