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Course11210129867 lectures

Optimization from fundamentals

Prof. Ankur A. Kulkarni · IIT Bombay

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Lecture 1A : Introduction Video
  2. Lecture 1B : Isoperimetric problem Video
  3. Lecture 1C : Review of real analysis (sequences and convergence) Video
  4. Lecture 2A : Bolzano-Weierstrass theorem and completeness axiom Video
  5. Lecture 2B : Open sets, closed sets and compact sets Video
  6. Lecture 2C : Continuity and Weierstrass theorem Video

Week 2

  1. Lecture 3A : Weierstrass theorem Video
  2. Lecture 3B : Different solution concepts Video
  3. Lecture 3C : Different types of constraints Video
  4. Lecture 4A : Taylor's theorem Video
  5. Lecture 4B: First order sufficient condition Video
  6. Lecture 4C : Second order necessary condition Video

Week 3

  1. Lecture 5A : Least square regression Video
  2. Lecture 5B : Least square regression (continued) Video
  3. Lecture 5C : Implicit function theorem Video
  4. Lecture 6A : Optimization with equality constraints and introduction to Lagrange multipliers - I Video
  5. Lecture 6B :Optimization with equality constraints and introduction to Lagrange multipliers - II Video
  6. Lecture 6C :Least norm solution of underdetermined linear system Video

Week 4

  1. Lecture 7A: Transformation of optimization problems - I Video
  2. Lecture 7B : Transformation of optimization problems - II Video
  3. Lecture 7C: Transformation of optimization problems - III Video
  4. Lecture 8A: Convex Analysis - I Video
  5. Lecture 8B: Convex Analysis - II Video
  6. Lecture 8C: Convex Analysis - III Video

Week 5

  1. Lecture 9A: Polyhedrons Video
  2. Lecture 9B: Minkowski-Weyl Theorem Video
  3. Lecture 9C: Linear Programming Problems Video
  4. Lecture 10A: Extreme points and optimal solution of an LP Video
  5. Lecture 10B: Extreme points and optimal solution of an LP (continued) Video
  6. Lecture 10C: Extreme points and basic feasible solutions Video

Week 6

  1. Lecture 11A: Equivalence of extreme point and BFS Video
  2. Lecture 11B: Equivalence of extreme point and BFS (continued) Video
  3. Lecture 11C: Examples of Linear Programming Video
  4. Lecture 12A: Weak and Strong duality Video
  5. Lecture 12B: Proof of strong duality Video
  6. Lecture 12C: Proof of strong duality (continued) Video

Week 7

  1. Lecture 13A: Farkas' lemma Video
  2. Lecture 13B: Max-flow Min-cut problem Video
  3. Lecture 13C: Shortest path problem Video
  4. Lecture 14A: Complementary Slackness Video
  5. Lecture 14B: Proof of complementary slackness Video

Week 8

  1. Lecture 14C: Tangent cones Video
  2. Lecture 15A:Tangent cones (continued) Video
  3. Lecture 15B: Constraint qualifications, Farkas' lemma and KKT Video
  4. Lecture 16A: KKT conditions Video
  5. Lecture 16B:Convex optimization and KKT conditions Video

Week 9

  1. Lecture 17A: Slater condition and Lagrangian Dual Video
  2. Lecture 17B: Weak duality in convex optimization and Fenchel dual Video
  3. Lecture 17C: Geometry of the Lagrangian Video
  4. Lecture 18A: Strong duality in convex optimization - I Video
  5. Lecture 18B: Strong duality in convex optimization - II Video
  6. Lecture 18C: Strong duality in convex optimization - III Video

Week 10

  1. Lecture 19A: Line search methods for unconstrained optimization Video
  2. Lecture 19B: Wolfe conditions Video
  3. Lecture 19C: Line search algorithm and convergence Video
  4. Lecture 20A: Steepest descent method and rate of convergence Video
  5. Lecture 20B: Newton's method Video
  6. Lecture 20C: Penalty methods Video

Week 11

  1. Lecture 21A: L1 and L2 Penalty methods Video
  2. Lecture 21B: Augmented Lagrangian methods Video
  3. Lecture 21C: Cutting plane methods Video
  4. Lecture 22: Interior point methods for linear programming Video

Week 12

  1. Lecture 23A: Dynamic programming: Inventory control problem Video
  2. Lecture 23B: Policy and value function Video
  3. Lecture 24A: Principle of optimality in dynamic programming Video
  4. Lecture 24B: Principle of optimality applied to inventory control problem Video
  5. Lecture 24C: Optimal control for a system with linear state dynamics and quadratic cost Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Bombay
Department
Mechanical Engineering
Teacher
Prof. Ankur A. Kulkarni
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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