# Optimization from fundamentals

- Institution: IIT Bombay
- Department: Mechanical Engineering
- Teacher: Prof. Ankur A. Kulkarni
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/112101298)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/112101298)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture 1A : Introduction](https://invisiblenetwork.ai/learn/nptel/112101298/919571c742c2) (Video)
2. [Lecture 1B : Isoperimetric problem](https://invisiblenetwork.ai/learn/nptel/112101298/51820e5040cb) (Video)
3. [Lecture 1C : Review of real analysis (sequences and convergence)](https://invisiblenetwork.ai/learn/nptel/112101298/a07f400ed5af) (Video)
4. [Lecture 2A : Bolzano-Weierstrass theorem and completeness axiom](https://invisiblenetwork.ai/learn/nptel/112101298/fcca4097be9d) (Video)
5. [Lecture 2B : Open sets, closed sets and compact sets](https://invisiblenetwork.ai/learn/nptel/112101298/974d8c28ae66) (Video)
6. [Lecture 2C : Continuity and Weierstrass theorem](https://invisiblenetwork.ai/learn/nptel/112101298/f8b02994242e) (Video)
7. [Lecture 3A : Weierstrass theorem](https://invisiblenetwork.ai/learn/nptel/112101298/9acf225bbf36) (Video)
8. [Lecture 3B : Different solution concepts](https://invisiblenetwork.ai/learn/nptel/112101298/ebbcaadb72f3) (Video)
9. [Lecture 3C : Different types of constraints](https://invisiblenetwork.ai/learn/nptel/112101298/271916fba828) (Video)
10. [Lecture 4A : Taylor's theorem](https://invisiblenetwork.ai/learn/nptel/112101298/1905de1ba5af) (Video)
11. [Lecture 4B: First order sufficient condition](https://invisiblenetwork.ai/learn/nptel/112101298/d22fa8f4262e) (Video)
12. [Lecture 4C : Second order necessary condition](https://invisiblenetwork.ai/learn/nptel/112101298/842eb9249823) (Video)
13. [Lecture 5A : Least square regression](https://invisiblenetwork.ai/learn/nptel/112101298/f0ce0b1b7277) (Video)
14. [Lecture 5B : Least square regression (continued)](https://invisiblenetwork.ai/learn/nptel/112101298/f06609f009f7) (Video)
15. [Lecture 5C : Implicit function theorem](https://invisiblenetwork.ai/learn/nptel/112101298/c62701c364e2) (Video)
16. [Lecture 6A : Optimization with equality constraints and introduction to Lagrange multipliers - I](https://invisiblenetwork.ai/learn/nptel/112101298/f3ea4258a7f9) (Video)
17. [Lecture 6B :Optimization with equality constraints and introduction to Lagrange multipliers - II](https://invisiblenetwork.ai/learn/nptel/112101298/b39b75b351f4) (Video)
18. [Lecture 6C :Least norm solution of underdetermined linear system](https://invisiblenetwork.ai/learn/nptel/112101298/fcf1e7e08698) (Video)
19. [Lecture 7A: Transformation of optimization problems - I](https://invisiblenetwork.ai/learn/nptel/112101298/033bb3353588) (Video)
20. [Lecture 7B : Transformation of optimization problems - II](https://invisiblenetwork.ai/learn/nptel/112101298/4a70c5b8e937) (Video)
21. [Lecture 7C: Transformation of optimization problems - III](https://invisiblenetwork.ai/learn/nptel/112101298/f3d22c903bdf) (Video)
22. [Lecture 8A: Convex Analysis - I](https://invisiblenetwork.ai/learn/nptel/112101298/e8736b604860) (Video)
23. [Lecture 8B: Convex Analysis - II](https://invisiblenetwork.ai/learn/nptel/112101298/2892aae69972) (Video)
24. [Lecture 8C: Convex Analysis - III](https://invisiblenetwork.ai/learn/nptel/112101298/62978db94d08) (Video)
25. [Lecture 9A: Polyhedrons](https://invisiblenetwork.ai/learn/nptel/112101298/8553ac7f9b42) (Video)
26. [Lecture 9B: Minkowski-Weyl Theorem](https://invisiblenetwork.ai/learn/nptel/112101298/6cb83a776743) (Video)
27. [Lecture 9C: Linear Programming Problems](https://invisiblenetwork.ai/learn/nptel/112101298/75fe6109f26f) (Video)
28. [Lecture 10A: Extreme points and optimal solution of an LP](https://invisiblenetwork.ai/learn/nptel/112101298/ce4e563902a3) (Video)
29. [Lecture 10B: Extreme points and optimal solution of an LP (continued)](https://invisiblenetwork.ai/learn/nptel/112101298/714e09bc8b88) (Video)
30. [Lecture 10C: Extreme points and basic feasible solutions](https://invisiblenetwork.ai/learn/nptel/112101298/e1ed291dd73b) (Video)
31. [Lecture 11A: Equivalence of extreme point and BFS](https://invisiblenetwork.ai/learn/nptel/112101298/95fb21e7f9d8) (Video)
32. [Lecture 11B: Equivalence of extreme point and BFS (continued)](https://invisiblenetwork.ai/learn/nptel/112101298/4f8345aa799e) (Video)
33. [Lecture 11C: Examples of Linear Programming](https://invisiblenetwork.ai/learn/nptel/112101298/d5aa2e8a0aa4) (Video)
34. [Lecture 12A: Weak and Strong duality](https://invisiblenetwork.ai/learn/nptel/112101298/0f9f567329f3) (Video)
35. [Lecture 12B: Proof of strong duality](https://invisiblenetwork.ai/learn/nptel/112101298/818d43922a72) (Video)
36. [Lecture 12C: Proof of strong duality (continued)](https://invisiblenetwork.ai/learn/nptel/112101298/64a97535cfb8) (Video)
37. [Lecture 13A: Farkas' lemma](https://invisiblenetwork.ai/learn/nptel/112101298/379884ce3808) (Video)
38. [Lecture 13B: Max-flow Min-cut problem](https://invisiblenetwork.ai/learn/nptel/112101298/d4a52e3f05ef) (Video)
39. [Lecture 13C: Shortest path problem](https://invisiblenetwork.ai/learn/nptel/112101298/d698ea03699a) (Video)
40. [Lecture 14A: Complementary Slackness](https://invisiblenetwork.ai/learn/nptel/112101298/6226284211ae) (Video)
41. [Lecture 14B: Proof of complementary slackness](https://invisiblenetwork.ai/learn/nptel/112101298/6bd59e9249d3) (Video)
42. [Lecture 14C: Tangent cones](https://invisiblenetwork.ai/learn/nptel/112101298/cc4225c2b18b) (Video)
43. [Lecture 15A:Tangent cones (continued)](https://invisiblenetwork.ai/learn/nptel/112101298/eea8568d3d6a) (Video)
44. [Lecture 15B: Constraint qualifications, Farkas' lemma and KKT](https://invisiblenetwork.ai/learn/nptel/112101298/4efe9622fc8d) (Video)
45. [Lecture 16A: KKT conditions](https://invisiblenetwork.ai/learn/nptel/112101298/334b755d80bb) (Video)
46. [Lecture 16B:Convex optimization and KKT conditions](https://invisiblenetwork.ai/learn/nptel/112101298/cc43c5e5bcc8) (Video)
47. [Lecture 17A: Slater condition and Lagrangian Dual](https://invisiblenetwork.ai/learn/nptel/112101298/e56106e5cf3e) (Video)
48. [Lecture 17B: Weak duality in convex optimization and Fenchel dual](https://invisiblenetwork.ai/learn/nptel/112101298/4d68061731fe) (Video)
49. [Lecture 17C: Geometry of the Lagrangian](https://invisiblenetwork.ai/learn/nptel/112101298/8eaafe8f6abf) (Video)
50. [Lecture 18A: Strong duality in convex optimization - I](https://invisiblenetwork.ai/learn/nptel/112101298/a4a385508d82) (Video)
51. [Lecture 18B: Strong duality in convex optimization - II](https://invisiblenetwork.ai/learn/nptel/112101298/aeed41a8b89b) (Video)
52. [Lecture 18C: Strong duality in convex optimization - III](https://invisiblenetwork.ai/learn/nptel/112101298/aecc10fd4199) (Video)
53. [Lecture 19A: Line search methods for unconstrained optimization](https://invisiblenetwork.ai/learn/nptel/112101298/9924ab00e4e9) (Video)
54. [Lecture 19B: Wolfe conditions](https://invisiblenetwork.ai/learn/nptel/112101298/c54ab9fc3dac) (Video)
55. [Lecture 19C: Line search algorithm and convergence](https://invisiblenetwork.ai/learn/nptel/112101298/0c0884688654) (Video)
56. [Lecture 20A: Steepest descent method and rate of convergence](https://invisiblenetwork.ai/learn/nptel/112101298/31610c5818fa) (Video)
57. [Lecture 20B: Newton's method](https://invisiblenetwork.ai/learn/nptel/112101298/aa73f51ad260) (Video)
58. [Lecture 20C: Penalty methods](https://invisiblenetwork.ai/learn/nptel/112101298/50ef0baa74c5) (Video)
59. [Lecture 21A: L1 and L2 Penalty methods](https://invisiblenetwork.ai/learn/nptel/112101298/b9d70b82a443) (Video)
60. [Lecture 21B: Augmented Lagrangian methods](https://invisiblenetwork.ai/learn/nptel/112101298/e354d3a7acdd) (Video)
61. [Lecture 21C: Cutting plane methods](https://invisiblenetwork.ai/learn/nptel/112101298/09ad55b5ccab) (Video)
62. [Lecture 22: Interior point methods for linear programming](https://invisiblenetwork.ai/learn/nptel/112101298/9776832bc814) (Video)
63. [Lecture 23A: Dynamic programming: Inventory control problem](https://invisiblenetwork.ai/learn/nptel/112101298/78f279e011fc) (Video)
64. [Lecture 23B: Policy and value function](https://invisiblenetwork.ai/learn/nptel/112101298/4586b83dc487) (Video)
65. [Lecture 24A: Principle of optimality in dynamic programming](https://invisiblenetwork.ai/learn/nptel/112101298/8fa051e5c380) (Video)
66. [Lecture 24B: Principle of optimality applied to inventory control problem](https://invisiblenetwork.ai/learn/nptel/112101298/a7d2ca444bb3) (Video)
67. [Lecture 24C: Optimal control for a system with linear state dynamics and quadratic cost](https://invisiblenetwork.ai/learn/nptel/112101298/de601ea3efed) (Video)