Convex Optimization

IIT Kanpur Course , Prof. Joydeep Dutta

Lecture 1: Convex Optimization

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Lecture Details :

Convex Optimization by Prof. Joydeep Dutta, Department of Mathematics and Statistics, IIT Kanpur. For more details on NPTEL visit http://nptel.iitm.ac.in

Course Description :

Basics of Convex Optimization - Basic facts of Convex Optimization - Basic properties of convex sets - Introduction to Polyhedral sets - Separation theorems for convex sets - Theorems of the alternative - Continuity and differentiability properties of convex functions - Non differentiable convex functions - Calculus of Sub differentials - Rockafeller-Pshenichny optimality condition - Properties of normals & projections - Computing the normal cone of inequality constraints - Tangent cone - Fenchel conjugate continues - Minimization of a convex function with convex inequality constraints is considered - Lagrangian Duality - Duality in connection with Linear Programming - Strong duality for convex problem

Pleasures of Linear Programming - Direction of descent - Extreme points of Linear Programming - Polyhedral sets & cones - Foundation of simplex methods - Fundamental theorem of Linear programming - Simplex methods - Simplex methods continued - Interior point methods - Interior point methods continued - Log barrier function - Primal-dual framework - Overview of interior point algorithm - Short step algorithm - Predictor-corrector method - Semi-definite programming - Saddle point type conditions for SDP - Approximate solutions - Descent direction for non-smooth functions - Minimization of difference convex functions - Minimization of difference convex functions continues - Concluding lecture

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