Sensitivity Analysis in Parametric Non-Convex Optimization

Sensitivity analysis plays a significant role in optimization models arising in applied sciences such as financial mathematics, risk analysis, signal processing, neural networks, and optimal control. In order to analyze the stability and qualitative behavior of solutions, parametrization of objective functions and constraints is frequently employed. While convex optimization problems ensure existence and stability of global optima under mild assumptions, non-convex optimization problems pose substantial theoretical challenges due to the possible absence of global optimal solutions. In this paper, we investigate sensitivity analysis for a class of generalized parametric non-convex optimization problems, where both the objective function and constraints may be non-convex. By introducing small perturbations through parameters, we analyze the behavior of local optimal solutions and derive results on the subdifferential of the optimal value function. Our approach extends several known results from convex parametric optimization to broader classes of generalized non-convex functions, including pseudo-convex and invex functions. We establish theoretical results with detailed proofs and validate our findings through numerical examples.