3 credits (3-0-0)
Pre-requisites: COL351 OR Equivalent
Overlaps with: MTL103, MTL704
Linear programming: introduction, geometry, duality, sensitivity analysis. Simplex method, Large scale optimization, network simplex. Ellipsoid method, problems with exponentially many constraints, equivalence of optimization and separation. Convex sets and functions – cones, hyperplanes, norm balls, generalized inequalities and convexity, perspective and conjugate functions. Convex optimization problems – quasi-convex, linear, quadratic, geometric, vector, semi-definite. Duality – Lagrange, geometric interpretation, optimality conditions, sensitivity analysis. Applications to approximation, fitting, statistical estimation, classification. Unconstrained minimization, equality constrained minimization and interior point methods. Integer Programming: formulations, complexity, duality. Lattices, geometry, cutting plane and branch and bound methods. Mixed integer optimization.