The optimization of deep neural networks (DNNs) for complex multivariate data analysis remains a major challenge due to high dimensionality, nonlinear dependencies, and data heterogeneity. This paper provides a comprehensive review of optimization strategies for DNNs applied to multivariate data. We highlight that achieving robust performance requires an integrated approach combining appropriate architecture design, advanced optimization techniques, automated configuration, and interpretability tools such as Explainable AI. Classical architectures (MLP, CNN, RNN, LSTM, GRU) remain effective for local and temporal pattern modeling, while transformers, tensor-based networks, and hierarchical or multi-stream models exhibit superior capabilities for capturing long-range and multi-level interactions. Gradient-based and evolutionary methods, together with AutoML, enable efficient and adaptive hyper parameter tuning, balancing accuracy, sparsity, and computational efficiency. Despite significant progress, challenges persist in handling heterogeneous and noisy data, ensuring scalability, and deploying models efficiently. This review emphasizes the importance of integrating architectural innovation, optimization strategies, and interpretability to enhance DNN performance for complex multivariate data.