Mathematical treatment of diverse optimization techniques.
1) Linear optimization: The geometry of linear programming, the simplex method for solving linear programming problems, Farkas' Lemma and infeasibility certificates, duality theory of linear programming.
2) Nonlinear optimization: Lagrange relaxation techniques, Newton method and gradient schemes for convex optimization.
3) Integer optimization: Ties between linear and integer optimization, total unimodularity, complexity theory, cutting plane theory.
4) Combinatorial optimization: Network flow problems, structural results and algorithms for matroids, matchings, and, more generally, independence systems.
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