When the function is wiggly, the variables are discrete, or the search space is huge: random walks that sample, meta-heuristics that explore, and branch-and-bound that prunes.
Metropolis-Hastings on the Rosenbrock function. Trajectory, autocorrelation, and the slide from sampling into simulated annealing.
Start here →Genetic algorithms, ant colony, simulated annealing as "structured random exploration." A skeptical look at what these actually buy you.
Explore →LP relaxation as a lower bound. Branch-and-bound on a 2-variable problem, pruning rules, and Gomory cuts that tighten the relaxation.
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