Lines of development, breakthroughs, applications and curiosities, and links
Antiquity
Greek mathematicians solve some
optimization problems that are related to their geometrical studies.
 300 bc
Euclid considers the minimal distance between a point a line, and
proves that a square has the greatest area among the rectangles with
given total length of edges
 200 bc Zenodorus
studies (according to Pappus & Theon) Dido's
Problem that has been described in Virgil's
Aeneid 19 bc
 100 bc Heron
proves in Catoprica that light travels between two points
through the path with shortest length when reflecting from a mirror
17th and 18th centuries
19th century
The first optimization algorithms are
presented. K.T.W. Weierstrass, J. Steiner, W.R.
Hamilton and C.G.J. Jacobi
further develop CoV.
 1806 A.M.
Legendre presents the least square method, which also J.C.F.
Gauss claims to have invented. Legendre made contributions in the
field of CoV, too
 1815 The idea of a (quasi) concave function appears in economics as
T.R. Malthus,
R. Torrens,
E. West, and
D.
Ricardo simultaneously introduce "the Law of
Dimishing Returns" for
production functions
 1826 J.B.J. Fourier formulates LPproblem for solving problems
arising in mechanics and probability theory
 1846 M. Faustmann presents the formula for the present value of the income stream of
forest rotation, the solution for the problem of maximizing Faustmann's formula was solved by B. Ohlin 1924
although some foresters were already aware of the correct solution in 1860's
 1847 A.L. Cauchy presents the gradient method
 1857 J.W. Gibbs shows that chemical equilibrium is an energy
minimum
The
marginalist revolution in economics during 1870s, e.g., the works
of L. Walras
and A. Cournot
shifts the focus of economists to utility maximizing individuals –
optimization becomes an integral part of economic theory.
20th century CoV is further developed, e.g., by O.
Bolza, C.
Caratheodory and G.A. Bliss.
 1902 J.
Farkas prsents his famous lemma which can be used in the proof of
KarushKuhnTucker theorem
 Convexity concepts are created: J.L.W.V.
Jensen introduces convex
functions in 1905, the idea has already appeared in the works of
J.S.
Hadamard (1883), O.L.
Hölder (1889), and O.
Stolz (1893). H.
Minkowski obtains the first results on convex sets in
1911, the earliest study on convex geometry was published by
H. Brunn in 1887

1917 H. Hancock publishes the first text book on optimization,
Theory of Minima and Maxima
 1917
biomathematician D.W. Thompson writes the book On Growth and Form, in
which he applies optimization to analyze the forms of living
organisms
 1925 H.C.M.
Morse presents his theory that generalizes CoV
 1928 F.P.
Ramsey applies CoV in his study on optimal economic growth, Ramsey's
exercise is resurrected in 50's as the field of optimal
growth theory starts to develop
 1931 J. Viner presents
the VinerWong envelope theorem

1932 K. Menger pressents a general
formulation of the travelling
salesman problem
 1939 L.V. Kantorovich presents LPmodel and an algorithm for solving
it. In 1975 Kantorovich and T.C. Koopmans get the Nobel memorial price of economics for their
contributions on LPproblem
After the
world war II optimization develops simultaneously with operations
research.
J. Von Neumann is an important person behind the
development of operations research. The field of algorithmic
research expands as electronic calculation develops.
 1944 J. von Neuman and O. Morgenstern solve sequential decision
problems by using the idea of dynamic programming.
A. Wald (1947) did related research. Another early
application of DP is presented by P.
Massé (1946) for reservoir management
 1947 G.
Dantzig,
who works for US airforces,
presents the Simplex method for solving LPproblems, von
Neumann establishes the theory of duality for LPproblems
 1949 the first international congress, International Symposium on
Mathematical Programming, on optimization is held in Chicago. The
number of papers presented in the congress is 34
1950s

1951 H.W. Kuhn and A.W.
Tucker
reinvent optimality conditions for nonlinear problems. F. John in 1948
and W. Karush in 1939 had presented similar conditions earlier

1951 H. Markowitz
presents his portfolio theory that is based on
quadratic optimization. In 1990 Markowitz receives the Nobel memorial
prize in economics
 1954 L.R.
Ford's and D.R. Fulkerson's research on network problems is a starting
point of research on combinatorial optimization
 Algorithms for
unbounded problems, such as quasiNewton and conjugate gradient
methods, are developed
Optimal control theory begins to develop as a separate
discipline from CoV. Space race gives
additional boost for research in optimal control theory
 1954 IEEE Control Systems
Society is founded
 1956 L.S.
Pontryagin's
research group presents maximum principle

1957
R.
Bellman presents the optimality principle
1960s

Zoutendijk (1960) presents the methods of feasible directions to
generalize the Simplex method for nonlinear programs. Rosen, Wolfe,
and Powell develop similar ideas

Sequential quadratic programming method is invented for the first time by Wilson 1963. Han 1975 and
Powell 1977 present it anew
1970  1973 Mathematical Programming Society
is founded
 1984 N. Karmarkar's
polynomial time algorithm for LPproblems begins a boom of interior
point methods.
The first polynomial time
algorithm for LP, the ellipsoid method, was already presented by
Khachiyan in 1979.
The complexity
analysis developed in 60s and 70s begins to influence to the theory of
optimization
 80s as computers become more efficient,
heuristic algorithms for global
optimization and large scale problems begin to gain popularity
 90s the use of interior point methods expands to semidefinite
optimization
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