[dajiaohuang]

Summary

Correct executable documentation examples without changing solver behavior:

• Select the DIFFCP backend with solver, and SCS/Clarabel within diffcp with solver_args["solve_method"] (including the case-sensitive "Clarabel"). Fix the solver guide, basic-usage guidance and constructor docstrings.
• Scope eps/max_iters to SCS and list Clarabel's actual tolerance/iteration settings.
• Remove the default-DIFFCP jax.vmap example and explain that built-in batching works with diffcp, while traced transformations require Moreau.

Evidence

On current master, a small DPP least-squares layer following the solver guide raises TypeError: ... unexpected keyword argument 'solver'. Passing solver=cp.CLARABEL as suggested elsewhere raises RuntimeError: Unknown solver. Executing the corrected construction, per-call override and Clarabel fallback snippets produces the expected solution and gradients. The default-backend vmap example raises TracerArrayConversionError; direct batching works.

Validation

Local Windows / Python 3.13, CVXPY 1.9.3, diffcp 1.1.9, SCS 3.3.1, Clarabel 0.11.1, Torch 2.14.1+cpu, JAX 0.11.2:

• Exact solver-guide snippets: base fails, corrected examples pass with a deterministic least-squares forward/backward oracle.
• Torch and JAX: unbatched/mixed-batch solver selection and overrides, analytic broadcast gradients, independent CVXPY solution and finite differences; simple batched DGP value/gradient oracle pass.
• pytest tests/test_jax.py tests/test_dual_variables_jax.py tests/test_torch.py tests/test_dual_variables.py tests/test_parse_args.py tests/test_readme_examples.py: 102 passed, 30 skipped, 3 failed. The failures are the existing three SCS gradchecks described in gradcheck tests fail with scs >= 3.3.0 (pass on 3.2.11) #244, also reproduced before edits; not changed here.
• Ruff 0.12.7 check on the three edited Python files and git diff --check pass. ASTs excluding docstrings are identical to master.
• Full pre-commit is not green: existing lint/format violations, optional-dependency/type-check failures and unrelated whitespace/EOF fixes. Unrelated autofixes were reverted; these three Python files also fail formatting on the base. Direct pyright with the isolated interpreter also reports existing typing/optional-backend errors.

MLX, Moreau, MPAX, CUDA/Julia and the documentation build were not run. No runtime implementation changes.

[SteveDiamond]

Reviewed the documentation and docstring changes against the current interfaces. The backend/solve_method distinction and batching guidance look reasonable.