Non linear function's optimization with global convergence on probabilistic approach by different latest techniques

From the Revolution of Mathematics by Newton's Calculus most of mathematicians, Scholars, researchers try to find optimization of Linear and Non Linear Problems (NLP). Up to 19th century most of researchers developed many techniques for solving linear types only. After Hilbert and Banach implementationsespecially in Functional Analysis and Theory of Approximations, scholars focused their mission in NLP. Kuhn-Tucker, wolf's identified and applied their own ideas to solve NLP. In this paper we try to solve NLP by Trust-Region methods, Rate Analysis of Unconstrained Methods, Linear Search Concepts and Direct Search Approach by Conjugate Gradient Concept with Globally convergence.