Max It or Miss It: Benchmarking LLM On Solving Extremal Problems

TL;DR

ExtremBench targets the largely unexplored capability of extremal reasoning under constraints in LLMs by transforming inequality-based proofs into standardized extrema problems that are numerically verifiable. The authors translate Chinese Mathematical Olympiad inequalities into optimization tasks, curate a dataset of $93$ problems ($62$ minimization, $31$ maximization), and benchmark open-source LLM families (Qwen3, GPT-OSS, DeepSeek) to reveal gaps between extremal-solving and general mathematical reasoning benchmarks like $AIME25$ and $MATH-500$. The study shows that high performance on traditional math benchmarks does not guarantee strong extremal-solving ability, and that larger models do not consistently outperform smaller ones, underscoring the need for domain-specific evaluation. The work proposes future directions including extending the transformation approach to other domains, multi-objective optimization, and targeted training strategies, with potential impact on automation in planning, control, and resource allocation. Overall, ExtremBench provides a principled framework to diagnose and improve LLMs' optimization reasoning capabilities beyond algebraic manipulation.

Abstract

Test-time scaling has enabled Large Language Models (LLMs) with remarkable reasoning capabilities, particularly in mathematical domains, through intermediate chain-of-thought (CoT) reasoning before generating final answers. However, the specific sources and mechanisms underlying these reasoning capabilities remain insufficiently understood. Optimization reasoning, i.e. finding extrema under constraints, represents a fundamental abstraction that underpins critical applications in planning, control, resource allocation, and prompt search. To systematically evaluate this capability, we introduce ExtremBench, a benchmark dataset for solving mathematical extremal problems, curated from inequality exercises used for Chinese Mathematical Olympiad and transformed into $93$ standardized extrema-finding problems. We conduct extensive evaluations across various state-of-the-art open-source model families, including the Qwen3, GPT-OSS, and DeepSeek. Our results reveal that LLMs' extremal-solving reasoning capabilities do not always align with those of current mathematical benchmarks such as AIME25 and MATH-500, with some models showing strong general mathematical reasoning but poor extremal-solving skills, and vice versa. This discrepancy highlights a critical gap in current evaluation practices and suggests that existing benchmarks may not comprehensively capture the full spectrum of mathematical reasoning abilities.

Figures (2)

• Figure 1: ExtremBench turns proof-style inequalities into equivalent extrema tasks, preserving reasoning challenge but enabling automatic evaluation.
• Figure 2: Evaluation results on ExtremBench and AIME25, sorted by the accuracy of ExtremBench.