The Pure Sub-gradient Method for Constraint Optimization problems

Abstract

In this paper, pure sub-gradient method has been investigated and a comprehensive study of high-level research knowledge about the concept of sub-gradient method have been developed. This method arises as a result of in-efficiency of direct method and conjugate gradient method to handle large sparse optimization problems, and therefore, sub-gradient optimization is one of the most important topics in the field of optimization. The method has been applied effectively in solving concave and convex optimization problems using programing system code language, as in the case of large-scale practical problems in the maximization of linear and nonlinear integer programming problem. This was achieved through the use of its properties and algorithms to taste the efficiency for convergence in finding an optimal solution to optimization problems. Hence, sub-gradient methods can be employed to effectively find solutions to large sparse optimization problems which are too large for direct methods or conjugate gradient methods to handle.