Subject Name: Convex optimization     Subject Code: SMAT430C

Objective of the course: Understanding the basics of convex analysis and solving convex optimization problems.

Outcome of the course: To able to solve convex optimization problems. Drive the Lagrange dual of the convex optimization problem.

Course outlines:
Unit-I: Affine and convex sets, Operations that preserve convexity, Separating and supporting hyper planes, Dual cones and generalized inequality.

Unit-II: Convex functions, First order and second order conditions of convex functions, Operations that preserve convexity, Conjugate and quasi convex function.
Log concave and log convex functions.

Unit-III: Optimization problems, Equivalent problems, Convex optimization problems, Linear optimization problems, Linear fractional programming, Qudratic
optimization problems, Least square, Second order cone programming, Geometric programming.

Unit-IV: Duality, The Lagrange dual function, KKT optimality conditions, Subdifferential of a convex functions, Gradient descent and subgradient descent method,
Nestervo's accelerated method, Newton's method.

Text book: S. Boyd and L.Vandenberghe, Convex Optimization. Cambridge University Press, 2004.

Reference books:
1: R. T. Rockafellar. Convex Analysis. Princeton University Press, 1996.
2: G. C. Calafiore and L. El Ghaoui, Optimization Models, Cambridge University Press, 2014.