dynamic starting point updating for guaranteed convergence in non-convex optimization

Traditional gradient descent algorithms often stagnate or diverge in nonconvex optimization landscapes due to their fixed initialization strategy. this extended abstract introduces a novel framework, dynamic starting point updating (dspu), that dynamically redefines the optimization origin based on local curvature and descent consistency. the method establishes a self-adaptive sequence of starting points, ensuring convergence even in non-convex and discontinuous objective functions. theoretical results show that dspu transforms the optimization trajectory into a quasi-convex path in parameter space, and empirical results demonstrate stable convergence across several benchmark functions and neural network training scenarios.