Mathematical Optimization Techniques For Improving Artificial Intelligence Model Performance

Abstract

Artificial Intelligence (AI) models increasingly depend on optimization procedures for determining model parameters, hyperparameters, regularization strengths, and training schedules. Although conventional optimization algorithms such as Stochastic Gradient Descent (SGD), Adam, and adaptive gradient methods have substantially improved neural-network training, they generally optimize a single objective or rely on manually selected hyperparameters. This paper proposes a Mathematical Multi-Objective Optimization Framework for Artificial Intelligence (MMO-AI) that jointly considers predictive loss, model complexity, parameter stability, and generalization-oriented sharpness during model optimization. The proposed framework formulates AI model training as a constrained multi-objective optimization problem and introduces a dynamically weighted objective that adapts according to validation performance and optimization stability. The method combines gradient-based parameter optimization with mathematical hyperparameter search and a curvature-aware regularization component. Unlike approaches that optimize only training loss or separately tune hyperparameters, MMO-AI integrates parameter optimization, regularization, and hyperparameter adaptation within a unified mathematical formulation. The proposed framework can be evaluated using image, tabular, and classification benchmarks against SGD, Adam, AdamW, random search, Bayesian optimization, and Sharpness-Aware Minimization (SAM). The experimental design measures accuracy, F1-score, loss, convergence speed, computational cost, and generalization gap. The framework provides a general mathematical strategy for improving AI model performance while maintaining a controllable balance between accuracy, complexity, and optimization stability.