Lec 20: Barrier method for solving linear programming problem, Augmented Lagrangian method.
Channel: Abhishek Gupta
Date: 2021-10-21

In this lecture, we will explore the barrier method for solving linear programming problems and introduce the augmented Lagrangian method. We will start by using log barrier function for solving linear programming problems with inequality constraints. We will discuss the optimality gap and stopping criterion.
Next, we will introduce the augmented Lagrangian method, which is a powerful technique for solving optimization problems with both equality and inequality constraints. We will explore the theory behind the augmented Lagrangian method and how it can be used to solve optimization problems efficiently. We then discuss a varation of augmented Lagrangian method, called method of multipliers, and how it is used to solve optimization problems.

This lecture series is from the Nonlinear Programming course that ran at The Ohio State University under the course number ECE 5759. The course builds on linear algebra and calculus to derive various algorithms for optimization in static and dynamic systems. The course is aimed at first-year graduate students, though senior undergraduate students with advanced knowledge of mathematics can also grasp the concepts discussed in the course. 
If you are interested in other courses taught by him, you can view them here:

Cybersecurity of Autonomous Systems (aimed at early graduate students): https://www.youtube.com/playlist?list=PL_Nk3YvgORJtMXvdpMD73okhm-MqQHqx0

Reinforcement Learning (aimed at very advanced PhD students): https://www.youtube.com/playlist?list=PL_Nk3YvgORJs1tCLQnlnSRsOJArj_cP9u

Game Theory and Mechanism Design (aimed at early PhD students): https://www.youtube.com/playlist?list=PL_Nk3YvgORJtEJrafhk9tb3E5qQRGHvCK

Signals and Systems (aimed at third year undergraduate students): https://www.youtube.com/playlist?list=PL_Nk3YvgORJuloGWq7YqhvQ9KV1ltwY8r

Feedback Control Systems (aimed at fourth year undergraduate students): https://www.youtube.com/playlist?list=PL_Nk3YvgORJv1sgMhuKZ-mlcidfLDl4zy

Prof. Abhishek Gupta is an Associate Professor in the Electrical and Computer Engineering department at The Ohio State University. He completed his Ph.D. in Aerospace Engineering (2014), MS in Applied Mathematics (2012), and MS in Aerospace Engineering (2011), all from University of Illinois at Urbana-Champaign (UIUC). Before coming to UIUC in 2009, he completed his undergraduate in Aerospace Engineering from Indian Institute of Technology, Bombay, India (2005-09). As part of his research, he contributes to probability theory, optimization methods, and practice of data-driven algorithms in various applications. He has developed theory to ascertain convergence of recursive stochastic algorithms. He has devised new algorithms to detect cyberattacks on autonomous systems, price transportation services, optimize fuel efficiency in vehicles, and optimize charging of electric vehicles using renewable energy.  His research has resulted in over 60 peer reviewed publications, 1 patent, and 2 pending patents. You can find more information about him and his research at https://gupta706.github.io/.