Learn · Transportation Network Analysis
Lecture 42 of 44Week 8
Lecture 42: Uniqueness and convex combinations method for two-link interactions
Prof. Hemant Gehlot · IIT Kanpur
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- Transportation Network Analysis, IIT Kanpur (at NPTEL)
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All the lectures
- 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
- Live Session 30-08-2025