A Sensitivity-Embedded Nonlinear Regression Operator: Mathematical Analysis and Optimization Properties

الملخص

    This paper describes a new direct yet adaptable nonlinear regression model with sensitivity functions. This method is an adaptive damping approach based on a transformation factor, rather than modifying the loss function or adding weights during optimization. This design allows the model to be sound and apparent. The model generates a nonlinear transformation factor by a continuous, bounded, and sublinear sensitivity function to prevent extreme values from becoming too high or too low. This factor automatically reduces the effect of characteristics with high values before estimation, allowing control of extreme values. Thus, even with the absence of penalty terms from the objective function, the model remains structurally regular. The loss function is slightly convex for regression coefficients and smooth for sensitivity coefficients, but not convex. This framework provides numerous optimization methods that fit the math problem with great success. The model remains robust even with highly or drastically variable values, and its forecasts align with those of ordinary models, which supports the argument. In this study, we present a new mathematical framework for nonlinear regression that models resilience as a built-in component rather than merely a means of estimation. The usefulness of this method lies in mathematical modeling, nonconvex optimization, and the study of complexity.