NOC:Optimization from Fundamentals

Lecture 1 - Introduction

Lecture 2 - Isoperimetric problem

Lecture 3 - Review of real analysis (sequences and convergence)

Lecture 4 - Bolzano-Weierstrass theorem and completeness axiom

Lecture 5 - Open sets, closed sets and compact sets

Lecture 6 - Continuity and Weierstrass theorem

Lecture 7 - Weierstrass theorem

Lecture 8 - Different solution concepts

Lecture 9 - Different types of constraints

Lecture 10 - Taylor's theorem

Lecture 11 - First order sufficient condition

Lecture 12 - Second order necessary condition

Lecture 13 - Least square regression

Lecture 14 - Least square regression (Continued...)

Lecture 15 - Implicit function theorem

Lecture 16 - Optimization with equality constraints and introduction to Lagrange multipliers - I

Lecture 17 - Optimization with equality constraints and introduction to Lagrange multipliers - II

Lecture 18 - Least norm solution of underdetermined linear system

Lecture 19 - Transformation of optimization problems - I

Lecture 20 - Transformation of optimization problems - II

Lecture 21 - Transformation of optimization problems - III

Lecture 22 - Convex Analysis - I

Lecture 23 - Convex Analysis - II

Lecture 24 - Convex Analysis - III

Lecture 25 - Polyhedrons

Lecture 26 - Minkowski-Weyl Theorem

Lecture 27 - Linear Programming Problems

Lecture 28 - Extreme points and optimal solution of an LP

Lecture 29 - Extreme points and optimal solution of an LP (Continued...)

Lecture 30 - Extreme points and basic feasible solutions

Lecture 31 - Equivalence of extreme point and BFS

Lecture 32 - Equivalence of extreme point and BFS (Continued...)

Lecture 33 - Examples of Linear Programming

Lecture 34 - Weak and Strong duality

Lecture 35 - Proof of strong duality

Lecture 36 - Proof of strong duality (Continued...)

Lecture 37 - Farkas' lemma

Lecture 38 - Max-flow Min-cut problem

Lecture 39 - Shortest path problem

Lecture 40 - Complementary Slackness

Lecture 41 - Proof of complementary slackness

Lecture 42 - Tangent cones

Lecture 43 - Tangent cones (Continued...)

Lecture 44 - Constraint qualifications, Farkas' lemma and KKT

Lecture 45 - KKT conditions

Lecture 46 - Convex optimization and KKT conditions

Lecture 47 - Slater condition and Lagrangian Dual

Lecture 48 - Weak duality in convex optimization and Fenchel dual

Lecture 49 - Geometry of the Lagrangian

Lecture 50 - Strong duality in convex optimization - I

Lecture 51 - Strong duality in convex optimization - II

Lecture 52 - Strong duality in convex optimization - III

Lecture 53 - Line search methods for unconstrained optimization

Lecture 54 - Wolfe conditions

Lecture 55 - Line search algorithm and convergence

Lecture 56 - Steepest descent method and rate of convergence

Lecture 57 - Newton's method

Lecture 58 - Penalty methods

Lecture 59 - L1 and L2 Penalty methods

Lecture 60 - Augmented Lagrangian methods

Lecture 61 - Cutting plane methods

Lecture 62 - Interior point methods for linear programming

Lecture 63 - Dynamic programming: Inventory control problem

Lecture 64 - Policy and value function

Lecture 65 - Principle of optimality in dynamic programming

Lecture 66 - Principle of optimality applied to inventory control problem

Lecture 67 - Optimal control for a system with linear state dynamics and quadratic cost