Topics in Applied Optimization

Course Outcomes

• Learn additional theory needed from calculus and linear algebra for optimization.
• Learn to model various applications from data science as an optimization problem.
• Learn to prove convergence estimates and complexity of the algorithms. 
• Learn to code optimization solvers efficiently using Python.
• Demonstrate expertise in applying optimization methods in research problems.

This course teaches numerical optimization techniques to UG and PG students.

• Unit 1:  Convex Sets, Convex Functions, Duality, Convex Optimization Problems (9 hours)
• Unit 2:  Steepest Descent, Newton methods, Quasi-Newton Methods, Interior Point Methods, Stochastic Optimization algorithms, Convergence Estimates (6 hours) 
• Unit 3:  Applications of optimization:  Recommender Systems, Support Vector Machines, Neural networks (9 hours)

References:

• Stephen Boyd and Lieven Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
• Ian Goodfellow, Yoshua Bengio and Aaron Courville, Deep Learning, MIT Press, 2016.

Weightages

• Assignments in theory: 15 marks, Mid Semester Examination: 25 marks, End Semester Examination: 30 marks, Assessment of four projects:  30 marks 

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