Chemical process optimization is crucial to maximize production efficiency and economic performance. Traditional methods, including gradient-based solvers, evolutionary algorithms, and parameter grid searches, become impractical when operating constraints are ill-defined or unavailable, requiring engineers to rely on subjective heuristics to estimate feasible parameter ranges. To address this constraint definition bottleneck, we present a multi-agent framework of large language model (LLM) agents that autonomously infer operating constraints from minimal process descriptions, then collaboratively guide optimization using the inferred constraints. Our AutoGen-based agentic framework employs OpenAI's o3 model, with specialized agents for constraint generation, parameter validation, simulation execution, and optimization guidance. Through two phases - autonomous constraint generation using embedded domain knowledge, followed by iterative multi-agent optimization - the framework eliminates the need for predefined operational bounds. Validated on the hydrodealkylation process across cost, yield, and yield-to-cost ratio metrics, the framework demonstrated competitive performance with conventional optimization methods while achieving better computational efficiency, requiring fewer iterations to converge. Our approach converged in under 20 minutes, achieving a 31-fold speedup over grid search. Beyond computational efficiency, the framework's reasoning-guided search demonstrates sophisticated process understanding, correctly identifying utility trade-offs, and applying domain-informed heuristics. This approach shows significant potential for optimization scenarios where operational constraints are poorly characterized or unavailable, particularly for emerging processes and retrofit applications.