Introduction to Optimization Algorithms

Learn the basic fundamentals of combinatorial and numerical optimization

What you’ll learn
✓ The concept of P-NP
✓ The foundations and intuitions of optimization algorithms
✓ The main algorithms used in combinatorial problems
✓ You will be able to think computationally regarding many problems

Requirements
● Bssic math knowledge

Description
Overview: This intensive 90-minute course provides a comprehensive theoretical journey through the world of numerical and computational optimization. Designed for those who seek to understand how machines solve complex problems, the seminar bridges the gap between classical calculus-based methods and modern evolutionary algorithms. We start by laying the groundwork with Computational Complexity (P vs. NP problems) and Big-O Notation, ensuring a solid understanding of the efficiency and limits of algorithmic performance.

Course Content: The lecture is structured to move from deterministic methods to stochastic exploration. We begin with Optimization with Derivatives, exploring how the slope of a function guides us to optima. However, as real-world problems often involve high Dimensionality and non-continuous search spaces, we transition into Numerical Optimization, discussing boundaries, constraints, and the distinction between discrete and continuous problems.

A central theme of the course is the balance between Exploration and Exploitation. We will analyze how Heuristics navigate the Search Space to avoid being trapped in Local Optima, aiming instead for the Global Optimum. The curriculum covers the design of Fitness Functions and the role of Hyperparameters in tuning algorithm behavior. We also delve into the “intelligence” of nature-inspired methods, such as Random Algorithms and Evolutionary Computing, explaining how these metaheuristics solve problems where traditional derivatives fail.

This course is an essential primer for anyone interested in the mathematical foundations of AI, operations research, and advanced engineering simulation.

Who this course is for
■ People who are interested in optimization algorithms