Template talk:Mathematical programming
I would suggest (at least) 5 main categories:
- Mathematical Foundations: Well-posed probems (existence and uniqueness, continuity of solutions w.r.t problem data), perturbation and sensitivity analysis (growth functions).
- partially ordered sets and lattices, Tarski's fixed-point theorem;
- complete metric spaces, closed graphs, convergence (perhaps including summability), Lipschitz continuity, contraction mappings, fixed point theorem of Banach, Kantorovich inequality;
- Convex and quasi-convex functions, inf compactness;
- matroids and greedy algorithms, oriented matroids, submodularity.
- Problem Classes (by popularity or by some categorical scheme, since LCP covers QP covers LP, etc.)
- Principles: objective functions, constraints, relaxations, penalty functions, Lagrangian function, duality thories.
- Algorithm complexity and problem complexity; convergence rates.
- Iterative Methods versus Algorithms versus Heuristics (Nelder-Meade simplex heuristic) [and then subtypes]),
- Applications or Modeling.
Perhaps it would be useful to adapt the organization of some comprehensive books from the 1970s, like those of Michel Minoux and Fisher (MIT)? (I'm trying to spur discussion.)Kiefer.Wolfowitz (talk) 18:10, 14 March 2010 (UTC)