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This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Global_optimization


00:02:52 1 General theory
00:12:16 2 Applications
00:13:42 3 Deterministic methods
00:13:56 3.1 Inner and outer approximation
00:14:21 3.2 Cutting-plane methods
00:15:02 3.3 Branch and bound methods
00:15:47 3.4 Interval methods
00:16:24 3.5 Methods based on real algebraic geometry
00:16:58 4 Stochastic methods
00:17:13 4.1 Direct Monte-Carlo sampling
00:18:33 4.2 Stochastic tunneling
00:19:06 4.3 Parallel tempering
00:20:35 5 Heuristics and metaheuristics
00:22:02 6 Response surface methodology-based approaches
00:22:28 7 See also



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SUMMARY
=======
Global optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set. It is usually described as a minimization problem because the maximization of the real-valued function



g
(
x
)


{\displaystyle g(x)}
is obviously equivalent to the minimization of the function



f
(
x
)
:=
(
−
1
)
⋅
g
(
x
)


{\displaystyle f(x):=(-1)\cdot g(x)}
.
Given a possibly nonlinear and non-convex continuous function



f
:
Ω
⊂


R


n


→

R



{\displaystyle f:\Omega \subset \mathbb {R} ^{n}\to \mathbb {R} }
with the global minima




f

∗




{\displaystyle f^{*}}
and the set of all global minimizers




X

∗




{\displaystyle X^{*}}
in



Ω


{\displaystyle \Omega }
, the standard minimization problem can be given as





min

x
∈
Ω


f
(
x
)
,


{\displaystyle \min _{x\in \Omega }f(x),}
that is, finding




f

∗




{\displaystyle f^{*}}
and a global minimizer in




X

∗




{\displaystyle X^{*}}
; where



Ω


{\displaystyle \Omega }
is a (not necessarily convex) compact set defined by inequalities




g

i


(
x
)
⩾
0
,
i
=
1
,
…
,
r


{\displaystyle g_{i}(x)\geqslant 0,i=1,\ldots ,r}
.
Global optimization is distinguished from local optimization by its focus on finding the minima or maxima over the given set, as opposed to finding local minima or maxima. Finding an arbitrary local minima is relatively straightforward by using classical local optimization methods. Finding the global minima of a function is far more difficult: analytical methods are frequently not applicable, and the use of numerical solution strategies often leads to very hard challenges.