The rapid growth in technology is propelling the world toward a smart future, and at the core of this transformation lies artificial intelligence (AI), which offers a powerful solution to a myriad of global problems. AI involves the application, implementation, and self-correction processes utilized in various domains. Machine learning, a subfield of AI, is the application of algorithms that enable systems to learn from data and improve performance without being explicitly programmed. However, not all data provides a convex solution, and optimization techniques are required to solve non-convex problems. As new problems emerge, researchers aim to convert non-convex optimization problems into convex ones, often by applying structured restrictions like sparsity or low rank, or by deliberately making the problem non-convex to better represent learning and prediction difficulties. Algorithms that work in high-dimensional environments or train non-linear models like tensor models and deep networks require such techniques, but these problems are notoriously NP-hard. One workaround involves relaxing non-convex issues into convex ones and then using conventional methods to solve the resulting relaxed optimization problems. The quality of the model is highly dependent on the effectiveness of optimization techniques. This paper explores various research works and focuses on solving non-convex optimization problems in machine learning.