Learn · Optimization from fundamentals
Lecture 40 of 67Week 7
Lecture 14A: Complementary Slackness
Prof. Ankur A. Kulkarni · IIT Bombay
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All the lectures
- Lecture 1A : Introduction
- Lecture 1B : Isoperimetric problem
- Lecture 1C : Review of real analysis (sequences and convergence)
- Lecture 2A : Bolzano-Weierstrass theorem and completeness axiom
- Lecture 2B : Open sets, closed sets and compact sets
- Lecture 2C : Continuity and Weierstrass theorem
- Lecture 3A : Weierstrass theorem
- Lecture 3B : Different solution concepts
- Lecture 3C : Different types of constraints
- Lecture 4A : Taylor's theorem
- Lecture 4B: First order sufficient condition
- Lecture 4C : Second order necessary condition
- Lecture 5A : Least square regression
- Lecture 5B : Least square regression (continued)
- Lecture 5C : Implicit function theorem
- Lecture 6A : Optimization with equality constraints and introduction to Lagrange multipliers - I
- Lecture 6B :Optimization with equality constraints and introduction to Lagrange multipliers - II
- Lecture 6C :Least norm solution of underdetermined linear system
- Lecture 7A: Transformation of optimization problems - I
- Lecture 7B : Transformation of optimization problems - II
- Lecture 7C: Transformation of optimization problems - III
- Lecture 8A: Convex Analysis - I
- Lecture 8B: Convex Analysis - II
- Lecture 8C: Convex Analysis - III
- Lecture 9A: Polyhedrons
- Lecture 9B: Minkowski-Weyl Theorem
- Lecture 9C: Linear Programming Problems
- Lecture 10A: Extreme points and optimal solution of an LP
- Lecture 10B: Extreme points and optimal solution of an LP (continued)
- Lecture 10C: Extreme points and basic feasible solutions
- Lecture 11A: Equivalence of extreme point and BFS
- Lecture 11B: Equivalence of extreme point and BFS (continued)
- Lecture 11C: Examples of Linear Programming
- Lecture 12A: Weak and Strong duality
- Lecture 12B: Proof of strong duality
- Lecture 12C: Proof of strong duality (continued)
- Lecture 13A: Farkas' lemma
- Lecture 13B: Max-flow Min-cut problem
- Lecture 13C: Shortest path problem
- Lecture 14A: Complementary Slackness
- Lecture 14B: Proof of complementary slackness
- Lecture 14C: Tangent cones
- Lecture 15A:Tangent cones (continued)
- Lecture 15B: Constraint qualifications, Farkas' lemma and KKT
- Lecture 16A: KKT conditions
- Lecture 16B:Convex optimization and KKT conditions
- Lecture 17A: Slater condition and Lagrangian Dual
- Lecture 17B: Weak duality in convex optimization and Fenchel dual
- Lecture 17C: Geometry of the Lagrangian
- Lecture 18A: Strong duality in convex optimization - I
- Lecture 18B: Strong duality in convex optimization - II
- Lecture 18C: Strong duality in convex optimization - III
- Lecture 19A: Line search methods for unconstrained optimization
- Lecture 19B: Wolfe conditions
- Lecture 19C: Line search algorithm and convergence
- Lecture 20A: Steepest descent method and rate of convergence
- Lecture 20B: Newton's method
- Lecture 20C: Penalty methods
- Lecture 21A: L1 and L2 Penalty methods
- Lecture 21B: Augmented Lagrangian methods
- Lecture 21C: Cutting plane methods
- Lecture 22: Interior point methods for linear programming
- Lecture 23A: Dynamic programming: Inventory control problem
- Lecture 23B: Policy and value function
- Lecture 24A: Principle of optimality in dynamic programming
- Lecture 24B: Principle of optimality applied to inventory control problem
- Lecture 24C: Optimal control for a system with linear state dynamics and quadratic cost