<p>Continuous Hopfield neural networks (CHN) have been widely applied in various optimization problems, due to their dynamical behavior that minimizes an associated energy function. This minimization process leads the network to an equilibrium point corresponding to the optimal solution. However, CHNs suffer from a critical limitation: Their convergence and solution quality depend sensitively on the choice of the parameters of the energy function of the network, which are often set arbitrarily. To address this limitation, we propose a novel and systematic framework for CHN parameter selection that integrates rigorous stability analysis with linear programming. Specifically, we derive linear constraints on the parameters from a comprehensive stability analysis, encoding conditions for stable convergence. We then formulate parameter selection as a linear programming problem and solve it using the simplex algorithm to find optimal parameter values. unlike the methods existing in the literature for the choice of CHN parameters, the proposed approach provides the theoretically grounded parameter settings that guarantee stable network convergence. We evaluated the proposed method on challenging combinatorial benchmarks, including task assignment and the traveling salesman problem. The results demonstrate that CHNs configured with our optimized parameters significantly outperform standard CHN implementations, yielding markedly better solution quality and convergence robustness. These results underscore the practical significance of our approach: by dramatically enhancing CHN reliability and effectiveness, our method enables a broader application of CHN in critical optimization domains such as logistics, scheduling, and AI, and lays the foundation for systematic parameter tuning in neural network based optimization methods.</p>