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From LP to IP: why integrality matters, LP relaxations, and why rounding fails.
Optimization
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Branch and bound: the workhorse algorithm for integer programming, explained with a complete knapsack example.- Published on
Cutting planes and branch-and-cut: tightening LP relaxations and how modern solvers solve integer programs.- Published on
An introduction to linear programming: definitions, standard form, geometric intuition, and practical examples.- Published on
The simplex method explained: slack variables, tableaux, pivoting, degeneracy, and a complete worked example.- Published on
Duality in linear programming: the dual problem, strong duality, complementary slackness, shadow prices, and sensitivity analysis.- Published on
Construction and improvement heuristics for the TSP: nearest neighbor, greedy, 2-opt, 3-opt, and Or-opt.- Published on
Metaheuristics for the TSP: simulated annealing, genetic algorithms, and ant colony optimization.- Published on
- Published on
A brief introduction to the Traveling Salesperson Problem (TSP)