# Convex Optimization

IIT Kanpur, , Prof. Joydeep Dutta

IIT Kanpur, , Prof. Joydeep Dutta

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

Sam

Sep 12, 2018

Excellent course helped me understand topic that i couldn't while attendinfg my college.

Dembe

March 29, 2019

Great course. Thank you very much.