[eng] One of the most importants problems has been tominimize functions. The history of optimization
and calculus of variations is tightly interwoven with the history of mathematics. The
field has drawn the attention of a remarkable range ofmathematical luminaries, beginning
with Newton and Leibniz, then initiated as a subject in its own right by the Bernoulli brothers
Jakob and Johann. The first major developments appeared in the work of Euler, Lagrange, and
Laplace. In the nineteenth century, Hamilton, Jacobi, Dirichlet, and Hilbert are but a few of
the outstanding contributors.
Nowadays, several related recent developments have stimulated new interest in the convex
optimization problems. The first is the recognition that interior-point methods, developed in
the 1980s to solve linear programming problems, can be used to solve convex optimization
problems as well. The second development is the discovery that convex optimization problems
(beyond least-squares and linear programs) are more prevalent in practice than was previously
thought. Since 1990 many applications have been discovered in areas such as automatic
control systems, estimation and signal processing, communications and networks, electronic
circuit design, data analysis and modeling, statistics, and finance. Convex optimization has also
foundwide application in combinatorial optimization and global optimization, where it is used
to find bounds on the optimal value, as well as approximate solutions. Hopfully many other
applications of convex optimization and calculus of variations are stillwaiting to be discovered.
There are great advantages to formulating a problem as a convex optimization problem. The
most basic advantage is that the problemcan then be solved, very reliably and efficiently, using
algorithms for convex optimization. These solution methods are reliable enough to be solved
with a computer. There are also theoretical or conceptual advantages of formulating a problem
as a convex optimization problem.