Lecture 3A : Weierstrass theorem

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Lecture 3B : Different solution concepts

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Lecture 3C : Different types of constraints

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Lecture 4A : Taylor's theorem

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Lecture 4B: First order sufficient condition

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Lecture 4C : Second order necessary condition

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Lecture 5A : Least square regression

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Lecture 5B : Least square regression (continued)

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Lecture 5C : Implicit function theorem

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Lecture 6A : Optimization with equality constraints and introduction to Lagrange multipliers - I

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Lecture 6B :Optimization with equality constraints and introduction to Lagrange multipliers - II

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Lecture 6C :Least norm solution of underdetermined linear system

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Lecture 7A: Transformation of optimization problems - I

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Lecture 7B : Transformation of optimization problems - II

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Lecture 7C: Transformation of optimization problems - III

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Lecture 8A: Convex Analysis - I

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Lecture 8B: Convex Analysis - II

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Lecture 8C: Convex Analysis - III

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Lecture 8C: Convex Analysis - III

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Lecture 9A: Polyhedrons

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Lecture 9B: Minkowski-Weyl Theorem

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Lecture 9C: Linear Programming Problems

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Lecture 10A: Extreme points and optimal solution of an LP

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Lecture 10B: Extreme points and optimal solution of an LP (continued)

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Lecture 10C: Extreme points and basic feasible solutions

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Lecture 11A: Equivalence of extreme point and BFS

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Lecture 11B: Equivalence of extreme point and BFS (continued)

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Lecture 11C: Examples of Linear Programming

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Lecture 12A: Weak and Strong duality

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Lecture 12B: Proof of strong duality

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Lecture 12C: Proof of strong duality (continued)

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Lecture 13A: Farkas' lemma

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Lecture 13B: Max-flow Min-cut problem

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Lecture 13C: Shortest path problem

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Lecture 14A: Complementary Slackness

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Lecture 14B: Proof of complementary slackness

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Lecture 14B: Proof of complementary slackness

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Lecture 14C: Tangent cones

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Lecture 15A:Tangent cones (continued)

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Lecture 15B: Constraint qualifications, Farkas' lemma and KKT

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Lecture 16A: KKT conditions

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Lecture 16B:Convex optimization and KKT conditions

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Lecture 17A: Slater condition and Lagrangian Dual

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Lecture 17B: Weak duality in convex optimization and Fenchel dual

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Lecture 17C: Geometry of the Lagrangian

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Lecture 18A: Strong duality in convex optimization - I

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Lecture 18B: Strong duality in convex optimization - II

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Lecture 18C: Strong duality in convex optimization - III

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Lecture 19A: Line search methods for unconstrained optimization

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Lecture 19B: Wolfe conditions

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Lecture 19C: Line search algorithm and convergence

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Lecture 20A: Steepest descent method and rate of convergence

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Lecture 20B: Newton's method

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Lecture 20C: Penalty methods

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Lecture 21A: L1 and L2 Penalty methods

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Lecture 21B: Augmented Lagrangian methods

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Lecture 21C: Cutting plane methods

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Lecture 22: Interior point methods for linear programming

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Lecture 23A: Dynamic programming: Inventory control problem

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Lecture 23B: Policy and value function

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Lecture 24A: Principle of optimality in dynamic programming

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Lecture 24B: Principle of optimality applied to inventory control problem

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Lecture 24C: Optimal control for a system with linear state dynamics and quadratic cost

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