Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Ankur A. Kulkarni
NPTEL Co-ordinating Institute : IIT Bombay
NPTEL Lecture Count : 67
NPTEL Course Size : 5.4 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
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