Lecture 1 - Course overview, and optimization formulations of fence and shortest path problems
Lecture 2 - Optimization formulations of shortest path and sensor problems and linear programming
Lecture 3 - Optimization formulations of knapsack, maximum coverage and travelling salesman problems
Lecture 4 - Alternative formulation of travelling salesman problem and introduction to complete matching problem
Lecture 5 - Optimization formulations of complete matching and scheduling problems
Lecture 6 - Continuation of scheduling problem; integer programming
Lecture 7 - Branch-and-bound algorithms
Lecture 8 - Analysis of algorithms and order of growth
Lecture 9 - Continuation of order of growth; polynomial-time algorithms
Lecture 10 - Continuation of polynomial-time algorithms; Dijkstra's algorithm
Lecture 11 - Minimum spanning tree, Kruskal's algorithm and Prim's algorithm
Lecture 12 - Approximation algorithm for travelling salesman problem and local search algorithms
Lecture 13 - Continuation of local search algorithms; vehicle routing problem with splitable demand
Lecture 14 - Continuation of vehicle routing problem with splittable demand; vehicle routing problem with unsplittable demand
Lecture 15 - Continuation of vehicle routing problem with splittable demand; vehicle routing problem with unsplittable demand
Lecture 16 - Continuation of genetic algorithms
Lecture 17 - Continuation of genetic algorithms
Lecture 18 - Introduction to traffic assignment (user equilibrium)
Lecture 19 - Continuous optimization (unconstrained)
Lecture 20 - Continuation of unconstrained optimization
Lecture 21 - Continuous optimization (constrained); first-order conditions for single variable problems
Lecture 22 - Continuation of first-order conditions for single variable problems; general first-order conditions
Lecture 23 - Continuation of general first-order conditions; case of nonnegativity and linear equality constraints
Lecture 24 - Sufficiency conditions and user equilibrium as an optimization problem
Lecture 25 - Equivalency and uniqueness conditions
Lecture 26 - System Optimization
Lecture 27 - Continuation of system optimization; Braess's paradox
Lecture 28 - Price of anarchy and optimization algorithms (golden section method)
Lecture 29 - Bisection method and convex combinations method
Lecture 30 - Continuation of convex combinations method
Lecture 31 - Solving UE using convex combinations method
Lecture 32 - Theory of discrete choice models; multinomial Logit model
Lecture 33 - Continuation of multinomial Logit model; multinomial Probit model
Lecture 34 - Satisfaction function and route choice
Lecture 35 - Continuation of route choice; Logit based loading
Lecture 36 - Continuation of Logit based loading; Probit based loading
Lecture 37 - Continuation of Probit based loading; stochastic user equilibrium
Lecture 38 - Continuation of stochastic user equilibrium
Lecture 39 - Method of successive averages
Lecture 40 - Continuation of method of successive averages; Two-link interactions in UE
Lecture 41 - Optimization formulation and first-order conditions for two-link interactions
Lecture 42 - Uniqueness and convex combinations method for two-link interactions
Lecture 43 - Generalization to multi-link interactions
