Convex optimization is a branch of mathematical optimization that deals with problems where the objective function is convex, meaning it curves upwards. In simpler terms, if you imagine a bowl shape, any line drawn between two points on the surface will lie above the surface. This property ensures that any local minimum is also a global minimum, making it easier to find the best solution. Many real-world problems, such as those in machine learning, finance, and engineering, can be framed as convex optimization problems. Techniques like gradient descent and Lagrange multipliers are commonly used to solve these problems efficiently, helping to optimize resources and improve decision-making.