Optimizing Gradient Methods for IoT Applications


The successful resolution of problems involving linear programming (LP) and nonlinear programming (NLP) is significant because of the breadth of their applications to real-world issues. There is no one method that can be used to determine which NLPs are the best overall. Nevertheless, on the other hand, the simplex algorithm, which has been the preeminent method for LPs for a number of decades, searches only on the boundary (vertices) and ignores the vast majority of the feasible region while doing so. This is because the simplex algorithm moves only on the boundary (vertices). In this article, we study two gradient-based methodologies that explore the entire feasible region. These methodologies guarantee faster convergence rates for both LP and NLP optimization problems, as well as problems related to the Internet of Things (IoT), such as Software-Defined Internet of Vehicles (SDIoV) and vehicular ad hoc networks. In addition, these methodologies explore the entire feasible region (VANETs). The gradient-simplex algorithm (GSA) for LPs is an algorithm that first moves inside the feasible region in the gradient direction to reduce the search space and then explores the reduced boundary to find an optimal solution. This algorithm is used to solve linear programming problems. The evolutionary-gradient algorithm (EGA), on the other hand, is designed for natural language processing (NLP), and it employs a population of evolving organisms to estimate gradients by gradually evolving into more effective solutions over time. The obtained numerical results, which are based on extensive simulations, demonstrate that both strategies offer effective solutions and outperform the methods that are considered to be state-of-the-art when applied to optimization problems with large feasible spaces. The report includes comparative results based on the application of the GSA to various sizes of SDIoV and VANETs.

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