``On the shoulders of giants''. A brief excursion into the history of mathematical programming (Q2866424)

The paper provides a very brief overview of the history of mathematical programming (a discipline also known as mathematical optimization).NEWLINENEWLINEThe first part deals with the foundational works such as Euler's and Lagrange's calculus of variations, the method of Lagrange multipliers, Farkas' lemma, Chebyshev's theory of approximation, Markov's moment problem, or Lyapunov's method.NEWLINENEWLINEThe second part focuses on linear optimization, whose roots can be traced back to Monge and de la Vallée Poussin. The main emphasis is put on the pioneering works of Kantorovich, Koopmans, Dantzig, and von Neumann.NEWLINENEWLINEThe third part discusses various topics in nonlinear optimization, such as the Kuhn-Tucker conditions (which generalize the method of Lagrange's multipliers to problems with inequality constraints), or the development of optimal control theory.NEWLINENEWLINEThe fourth part shortly indicates the main research directions in the 1960s and 1970s, including convex analysis, the investigation of the complexity of the simplex algorithm, or various iterative methods.NEWLINENEWLINEThe paper also contains brief biographical sketches of the most important figures, and an extensive list of references.