Optimization Theory and Algorithms

This course helps students understand optimization, which means finding the best possible solution to an engineering problem from many available options. In real life, engineers often need to minimize cost, time, energy, or error, or maximize performance, efficiency, or reliability. This course explains how such problems are solved in a systematic and mathematical way.

The course starts with the basics of optimization, including:

• Unconstrained optimization, where solutions are found without any restrictions.

• Constrained optimization, where solutions must satisfy certain limits or conditions (such as physical, safety, or design constraints).

Students will learn why these problems arise in engineering and how to mathematically model them so they can be solved using optimization techniques.The main focus of the course is on modern and practical optimization algorithms that are widely used today in engineering, data science, control systems, machine learning, and operations research. The course explains not just how these algorithms work, but also why they work, so students can clearly understand their logic.To support this, the course provides strong theoretical foundations in an easy-to-understand manner. This helps students connect the math with real-world applications instead of memorizing formulas.

In addition, the course includes illustrative programming assignments, where students implement optimization algorithms using code. These hands-on exercises help students:

• Visualize how optimization methods converge to a solution

• Gain confidence in applying theory to practical problems

• Develop problem-solving and programming skills that are useful in real engineering work

By the end of the course, students will be able to formulate optimization problems, choose suitable algorithms, and implement solutions efficiently.

Source: NPTEL NOC IITM [Youtube Channel]