High-performance concrete requires complex mix design decisions involving interdependent variables and practical constraints. While data-driven methods have improved predictive modeling for forward design in concrete engineering, inverse design remains limited, especially when some variables are fixed and only the remaining ones must be inferred. This study proposes a cooperative neural network framework for the partial inverse design of high-performance concrete. The framework integrates an imputation model with a surrogate strength predictor and learns through cooperative training. Once trained, it generates valid and performance-consistent mix designs in a single forward pass without retraining for different constraint scenarios. Compared with baseline models, including autoencoder models and Bayesian inference with Gaussian process surrogates, the proposed method achieves R-squared values of 0.87 to 0.92 and substantially reduces mean squared error by approximately 50% and 70%, respectively. The results show that the framework provides an accurate and computationally efficient foundation for constraint-aware, data-driven mix proportioning.