Objective-Prescribed Escape for Gradient Descent in Non-Convex Optimization

Gradient-based optimization methods may stagnate in local attraction basins when applied to non-convex objective functions. This paper proposes a deterministic, first-order escape mechanism that preserves standard gradient descent as the default optimization procedure. An objective-prescription mechanism is activated only when stagnation is detected. Rather than modifying the gradient direction or the objective landscape, the proposed approach prescribes a strictly decreasing evolution of the objective function and determines the step size required to realize the prescribed objective value along the current gradient direction. The resulting escape step is obtained by solving a scalar nonlinear equation, which may admit multiple solutions. Small displacements are discarded, and deterministic root-selection strategies are considered to identify an effective escape step. After this temporary intervention, the algorithm immediately returns to standard gradient descent with its predefined step size. Numerical experiments on one-dimensional non-convex benchmark functions demonstrate that the proposed mechanism can escape local attraction basins and reach the global minimum from a broad range of initial conditions. The results provide an initial numerical validation of the proposed deterministic, objective-prescribed escape principle.