Convex optimization is a subfield of
mathematical optimization that studies the problem of minimizing
convex functions over
convex sets (or, equivalently, maximizing
concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms,
whereas mathematical optimization is in general
NP-hard.
Convex optimization has applications in a wide range of disciplines, such as automatic
control systems, estimation and
signal processing, communications and networks, electronic
circuit design, data analysis and modeling,
finance,
statistics (
optimal experimental design), and
structural optimization, where the approximation concept has proven to be efficient.
With recent advancements in computing and
optimization algorithms, convex programming is nearly as straightforward as
linear programming.
Definition
A convex optimization problem is an
optimization problem
In mathematics, computer science and economics, an optimization problem is the problem of finding the ''best'' solution from all feasible solutions.
Optimization problems can be divided into two categories, depending on whether the variables ...
in which the objective function is a
convex function and the
feasible set is a
convex set. A function
mapping some subset of
into
is convex if its domain is convex and for all