COT6505 Computational Methods Analysis I

Instructor: Guo-Jun Qi

Office hour: 2-3pm Thursday HEC 318

In this course we will focus on fundamental theories and algorithms in convexity, duality, and convex optimization algorithms. The students will learn the core analytical and algorithmic issues of the conditions of the existence of the optimal solutions, optimality conditions, duality, and Lagrange multiplier theories built upon the fundamental principles that can be easily visualized and understood.  The students will also have opportunity to learn the applications of optimization problems into machine learning, computer vision, and data analytics.

 

Textbook:

D. P. Dertsekas, A. Nedic and A. E. Ozdaglar. Convex Analysis and Optimization. Athena Scientific (2003).

Recommended Textbooks:

S. Boyd and L. Vandenberghe. Convex Optimization.  Cambridge University Press (2004).

 

Topics (subject to change):

        Review of calculus and real analysis

        Convexity, optimality condition and existence of optimal solutions

        Polyhedral Convexity

        Lagrange Multipliers and duality

        Conjugate duality

        Practical algorithms for unconstrained and constrained optimization problems

 

Grading policy (subject to change):

Homework 50% + final project 50%

Machine Problem is announced here.