# A Primer to Mathematical Optimization

- Institution: IIT(BHU) Varanasi
- Department: Mathematics
- Teacher: Prof. Debdas Ghosh
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111104165)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111104165)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

In this era of Machine Learning and Data Science, students often crave for learning the basic tools of optimization theory because machine learning ideas essentially exploit the power of Numerical Linear Algebra, Optimization, and Statistics. The primary aim of this course is to hand over a complete readymade package for beginners in mathematical optimization. 'Complete' in the sense of its mathematical orientation, geometrical explanation, problem-solution sheets, and tutorial sheets. After attending this course, students will get to know the standard methods, and basic and modern results in optimization. The concepts will be explained not only with mathematical rigor but also with geometrical essence so that students feel optimization is fun. The course covers mathematical foundation for optimization and basic techniques of unconstrained and constrained optimization problems.

Intended audience: Third Year Undergraduates of Mathematics / Computer Science / Electrical / Mechanical Engineering

Prerequisites: Calculus, Linear Algebra, Coordinate Geometry

## Lectures

1. [Lecture 01: Introduction and Histroy on the Development of Optimization Theory](https://invisiblenetwork.ai/learn/nptel/111104165/18cb6bd76b66) (YouTube)
2. [Lecture 02: Tools from Linear Algebra](https://invisiblenetwork.ai/learn/nptel/111104165/38efd93fafd7) (YouTube)
3. [Lecture 03: Tools from Linear Algebra](https://invisiblenetwork.ai/learn/nptel/111104165/c9188e8a3b17) (YouTube)
4. [Lecture 04 : Tools for calculus of several variables](https://invisiblenetwork.ai/learn/nptel/111104165/da40d66469be) (YouTube)
5. [Lecture 05 : Tools from calculus of several variables](https://invisiblenetwork.ai/learn/nptel/111104165/4bacf75523e9) (YouTube)
6. [Lecture 6: Order of Convergence](https://invisiblenetwork.ai/learn/nptel/111104165/7ebb7f41c306) (YouTube)
7. [Lecture 7: Continuity](https://invisiblenetwork.ai/learn/nptel/111104165/bf52b066b04f) (YouTube)
8. [Lecture 8 & 9 : Partial and Directional Derivatives and Differentiability](https://invisiblenetwork.ai/learn/nptel/111104165/e383a6a90e1a) (YouTube)
9. [Lecture - 10 : Taylor's Theorem](https://invisiblenetwork.ai/learn/nptel/111104165/4608babfb3f8) (YouTube)
10. [Lecture - 11 : Convex Sets & Convexity Preserving Operations](https://invisiblenetwork.ai/learn/nptel/111104165/d2e773b37dad) (YouTube)
11. [Lecture - 12 : Separation Result](https://invisiblenetwork.ai/learn/nptel/111104165/087e9bebb70c) (YouTube)
12. [Lecture - 13 & 14 : Theorems of Alternatives](https://invisiblenetwork.ai/learn/nptel/111104165/7e0ae2d3112e) (YouTube)
13. [Lecture - 15 : Convex Functions](https://invisiblenetwork.ai/learn/nptel/111104165/68d0824d55dd) (YouTube)
14. [Lecture -16 : Properties and Zeroth Order Characterization of Convex Functions](https://invisiblenetwork.ai/learn/nptel/111104165/56a697e3d023) (YouTube)
15. [Lecture - 17 : First-Order and Second-Order Characterization of Convex Functions](https://invisiblenetwork.ai/learn/nptel/111104165/e850fbb31f1d) (YouTube)
16. [Lecture - 18 : Convexity Preserving Operations](https://invisiblenetwork.ai/learn/nptel/111104165/adf60fd8b90a) (YouTube)
17. [Lecture - 19 : Optimality and Coerciveness](https://invisiblenetwork.ai/learn/nptel/111104165/bf70903dc148) (YouTube)
18. [Lecture 20 part 1: First Order Optimality Condition](https://invisiblenetwork.ai/learn/nptel/111104165/7eefe1617f16) (YouTube)
19. [Lecture 20 part 2: Second Order Optimality Conditions](https://invisiblenetwork.ai/learn/nptel/111104165/cc80fddd2f8e) (YouTube)
20. [Lecture 21: General Structure of Unconstrained Optimization Algorithms](https://invisiblenetwork.ai/learn/nptel/111104165/4c8ec4411c7a) (YouTube)
21. [Lecture 22: Inexact Line Search](https://invisiblenetwork.ai/learn/nptel/111104165/165795a6da6b) (YouTube)
22. [Lecture 23 & 24: Global Convergence of Descent Methods](https://invisiblenetwork.ai/learn/nptel/111104165/76ec6eeb165b) (YouTube)
23. [Lecture 25: Where do Descent Methods Converge?](https://invisiblenetwork.ai/learn/nptel/111104165/a246a8e3d539) (YouTube)
24. [Lecture - 26 : Scaling Of Variables](https://invisiblenetwork.ai/learn/nptel/111104165/51b8c82bc41d) (YouTube)
25. [Lecture - 27 : Practical Stopping Criteria](https://invisiblenetwork.ai/learn/nptel/111104165/fece5d149a5d) (YouTube)
26. [Lecture - 28 & 29 : Steepest Descent Method](https://invisiblenetwork.ai/learn/nptel/111104165/d91a2911e86c) (YouTube)
27. [Lecture - 30, 31 & 32 : Newton's Method](https://invisiblenetwork.ai/learn/nptel/111104165/b9f5f3d68bb5) (YouTube)
28. [Lecture - 33, 34 & 35](https://invisiblenetwork.ai/learn/nptel/111104165/303326421dd4) (YouTube)
29. [Lecture - 36 & 37](https://invisiblenetwork.ai/learn/nptel/111104165/d496336e39ba) (YouTube)
30. [Lecture - 38 Part 1](https://invisiblenetwork.ai/learn/nptel/111104165/f9ecd1a5a515) (YouTube)
31. [Lecture - 38 Part 2](https://invisiblenetwork.ai/learn/nptel/111104165/bae9a5419edf) (YouTube)
32. [Lecture - 39 : A Revisit to Lagrange Multipliears Method](https://invisiblenetwork.ai/learn/nptel/111104165/62e287f5c3e7) (YouTube)
33. [Lecture - 40 : Special Cones for Contrained Optimization](https://invisiblenetwork.ai/learn/nptel/111104165/62639c081b20) (YouTube)
34. [Lecture - 41 : Tangent Cone](https://invisiblenetwork.ai/learn/nptel/111104165/49bb51523ace) (YouTube)
35. [Lecture - 42 & 43 : First-Order KKT Optimality Conditions](https://invisiblenetwork.ai/learn/nptel/111104165/da02d65fccc9) (YouTube)
36. [Lecture 44 : Second-Order KKT Optimality Conditions](https://invisiblenetwork.ai/learn/nptel/111104165/3a319b392bb7) (YouTube)
37. [Lecture 45 : Constraint Qualifications](https://invisiblenetwork.ai/learn/nptel/111104165/06f0f1d3bfd7) (YouTube)
38. [Lecture 46, 47, 48, 49 & 50 : Lagrangian Duality Theory](https://invisiblenetwork.ai/learn/nptel/111104165/c6dca842c1fc) (YouTube)
39. [Lecture 51, 52 & 53 : Methods for Linearly Constrained Problems](https://invisiblenetwork.ai/learn/nptel/111104165/26420899e733) (YouTube)
40. [Lecture 54 : Interior-Point Method for QPP](https://invisiblenetwork.ai/learn/nptel/111104165/4ae7cdbd036e) (YouTube)
41. [Lecture 55 : Penalty Methods](https://invisiblenetwork.ai/learn/nptel/111104165/a6d0f288afb8) (YouTube)
42. [Lecture 56 : Sequential Quadratic Programming Method](https://invisiblenetwork.ai/learn/nptel/111104165/22886fad6554) (YouTube)