Constraints exploration method for convex optimization

Abstract

In this paper, we represent a method which based on the violated constraints by the unconstrained minimum of the objective function of the convex programming problem for exploring, locating and computing the optimal solution of the problem without using additional information as have been done in most of the favorite established methods in literature. In order to obtain the unconstrained minimum we used the steepest descent method, where the step size has playing an important role. There are several well-known procedures to determine the best step size. In this research we used the fixed-range step size procedure for fast-converge to the solution. The results show that our exploration method never fails to obtain the optimal solution.