Convex Optimization

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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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