This paper investigates the performance of Large Language Models (LLMs) as generative optimizers for solving constrained multi-objective regression tasks, specifically within the challenging domain of inverse design (property-to-structure mapping). This problem, critical to materials informatics, demands finding complex, feasible input vectors that lie on the Pareto optimal front. While LLMs have demonstrated universal effectiveness across generative and reasoning tasks, their utility in constrained, continuous, high-dimensional numerical spaces tasks they weren't explicitly architected for remains an open research question. We conducted a rigorous comparative study between established Bayesian Optimization (BO) frameworks and a suite of fine-tuned LLMs and BERT models. For BO, we benchmarked the foundational BoTorch Ax implementation against the state-of-the-art q-Expected Hypervolume Improvement (qEHVI, BoTorchM). The generative approach involved fine-tuning models via Parameter-Efficient Fine-Tuning (PEFT), framing the challenge as a regression problem with a custom output head. Our results show that BoTorch qEHVI achieved perfect convergence (GD=0.0), setting the performance ceiling. Crucially, the best-performing LLM (WizardMath-7B) achieved a Generational Distance (GD) of 1.21, significantly outperforming the traditional BoTorch Ax baseline (GD=15.03). We conclude that specialized BO frameworks remain the performance leader for guaranteed convergence, but fine-tuned LLMs are validated as a promising, computationally fast alternative, contributing essential comparative metrics to the field of AI-driven optimization. The findings have direct industrial applications in optimizing formulation design for resins, polymers, and paints, where multi-objective trade-offs between mechanical, rheological, and chemical properties are critical to innovation and production efficiency.