AI
LLMs can find near-optimal numerical solutions but remain unreliable alone
A study comparing language models with deterministic numerical solvers finds that LLMs can recognize useful optimization structure and sometimes produce near-optimal solutions, but their outputs often fail through numerical inaccuracies, constraint violations, or formatting errors. Reliability declines as problem dimensions grow and depends on the optimization structure. An iterative refinement process using targeted feasibility and quality feedback improves validity and extends the workable range. The authors therefore favor hybrid systems in which LLM reasoning is checked by deterministic numerical verification.
Editorial summary · Publisher article
What matters
- The evaluation covers convex optimization, fractional programming, and constrained projection.
- The study separates solution quality from execution and formatting failures.
- Iterative refinement improves reliability but does not eliminate persistent numerical and structural errors.
Context & caveats
- The supplied material summarizes a preprint abstract and does not provide the underlying model-by-model results.
Why this made the edition
The study directly tests LLMs as numerical optimizers against deterministic reference solvers and distinguishes near-optimal solutions from execution failures. It reports concrete limitations and an improvement mechanism, making it useful to readers evaluating LLM reliability in technical workflows.
Source material