arXiv:2606.31182v1 Announce Type: new Abstract: Recent work shows that LLM agents can improve sharp-constant inequalities by searching for extremal constructions, which yield upper bounds. We address the complementary side: a lower bound holds for every admissible function and follows from a convex relaxation of the nonconvex problem, with tighter relaxations giving stronger bounds. We instantiate the autoresearch paradigm to discover such relaxations: a coding agent proposes valid tightening constraints, a theory agent verifies each one and searches for counterexamples, and every reported bou
Advances in LLMs and AI agent architectures are enabling new approaches to complex computational problems, making the automation of discovery processes viable.
This development represents a significant step towards AI autonomously improving mathematical and computational methods, potentially accelerating breakthroughs across various scientific and engineering fields.
The process of discovering and tightening convex relaxations, previously a human-intensive task, can now be partly automated and enhanced by AI agents.
- · AI research labs
- · Optimization software developers
- · Industries relying on complex optimization (e.g., logistics, finance, engineerin
- · Traditional manual methods of mathematical discovery
- · Researchers unwilling to adopt AI-assisted tools
AI agents accelerate the discovery of more efficient algorithms and tighter bounds for optimization problems.
Improved optimization techniques lead to more efficient resource allocation, design, and decision-making in various industries.
The principle of AI-assisted discovery extends to other domains of mathematical and scientific research, reshaping academic workflows.
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Read at arXiv cs.AI