• Peeyush Kumar
• Arvind Kumar Sah

The modulus of Tykhonov well-posedness quantifies the stability and uniqueness of solutions to optimization problems, particularly in the context of constrained non-convex optimization. A problem is Tykhonov well-posed if it has a unique minimizer, and every minimizing sequence converges to this minimizer. The modulus measures the rate at which the objective function grows away from the minimizer, providing a metric for the "degree" of well-posedness. For constrained non-convex problems, the modulus is influenced by the curvature of the objective function and the geometry of the feasible set defined by constraints. It is typically analyzed through conditions like strong convexity or weaker growth conditions near the solution. In non-convex settings, the modulus may only hold locally, and its computation often involves the second-order properties of the objective and constraints, such as the Hessian or constraint qualifications. The modulus is critical for assessing convergence rates of algorithms and robustness to perturbations, with applications in machine learning, control theory, and inverse problems.

Tykhonov well-posedness, Function, Non-convex, Control theory etc.

"MODULUS OF TYKHONOV WELL-POSEDNESS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.11, Issue 3, page no.l410-l414, March-2024, Available :http://www.jetir.org/papers/JETIR2403B46.pdf

"MODULUS OF TYKHONOV WELL-POSEDNESS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.11, Issue 3, page no. ppl410-l414, March-2024, Available at : http://www.jetir.org/papers/JETIR2403B46.pdf