Batch solve

[govindchari]

Two benchmarks were run against the CUDA/cuDSS backend:

1. Small SOCP batch test: 100 perturbed variants of cvxpy_qoco.socp_0, a tiny SOCP with n = 3, m = 3, p = 2, and one SOC. Batched cuDSS reduced factor+solve time from 0.057893s to
   0.001314s, about 44x faster inside cuDSS, but end-to-end solve time was effectively unchanged: 3.508s serial vs 3.519s batch.
2. PDG batch test: 100 variants of a larger PDG problem, perturbing initial-condition entries in b, with n = 2698 and nsoc = 598. Batched cuDSS reduced factor+solve time from 0.862373s to
   0.328448s, about 2.6x faster inside cuDSS, and improved end-to-end solve time modestly: 9.074s serial vs 8.694s batch, about 4.4% faster excluding setup.

Main finding: the cuDSS batch API works and speeds up the linear algebra calls, but full solver speedup is limited because most runtime is still spent in QOCO-side per-item work outside
cuDSS. Batch setup is also currently expensive because it initializes a full QOCOSolver for every batch item.

The QOCO-side work can be batched if the batch API is redesigned around shared problem structure plus batched state arrays. Good candidates:

• Shared once per batch: dimensions, cone structure, sparsity, transposes, KKT symbolic structure, index maps, cuDSS analysis.
• Per item but stored contiguously: x, s, y, z, rhs, kktres, WtW, lambda, Ds, objective/residual scalars, status flags.
• Batched GPU kernels: residual computation, objective, mu, stopping metrics, NT scaling, RHS construction, centering, line search, iterate updates, and solution copy-out.

The biggest wins would likely come from batching the per-iteration loops currently visible around compute_kkt_residual, compute_objective, compute_mu, compute_nt_scaling, and
construct_kkt_aff_rhs in algebra/cuda/cudss_backend.cu:1790. Those are currently dispatched per solver item, even though the items have common dimensions and sparsity.

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Download Benchmark Artifacts

Benchmark Summary

Problems Solved

Dataset	Main Solved	Diff Solved	Main Iters	Diff Iters	Main IR Iters	Diff IR Iters
cutest	43 / 62	43 / 62	1069	1069	2301	2301
misc	1 / 3	1 / 3	15	15	2	2
mm	136 / 138	136 / 138	2615	2615	4420	4420
mpc	63 / 64	63 / 64	480	480	587	587

[github-actions]

Download Benchmark Artifacts

Benchmark Summary

Problems Solved

Dataset	Main Solved	Diff Solved	Main Iters	Diff Iters	Main IR Iters	Diff IR Iters
cutest	43 / 62	43 / 62	1069	1069	2301	2301
misc	1 / 3	1 / 3	15	15	2	2
mm	136 / 138	136 / 138	2615	2615	4420	4420
mpc	63 / 64	63 / 64	480	480	587	587