Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic Global Optimization Algorithms: A Systematic Formal Approach   As we know, some global optimization problems cannot be solved using analytic
methods, so numeric/algorithmic approaches are used to find near to the optimal
solutions for them. A stochastic global optimization algorithm (SGoal) is an
iterative algorithm that generates a new population (a set of candidate
solutions) from a previous population using stochastic operations. Although
some research works have formalized SGoals using Markov kernels, such
formalization is not general and sometimes is blurred. In this paper, we
propose a comprehensive and systematic formal approach for studying SGoals.
First, we present the required theory of probability (\sigma-algebras,
measurable functions, kernel, markov chain, products, convergence and so on)
and prove that some algorithmic functions like swapping and projection can be
represented by kernels. Then, we introduce the notion of join-kernel as a way
of characterizing the combination of stochastic methods. Next, we define the
optimization space, a formal structure (a set with a \sigma-algebra that
contains strict \epsilon-optimal states) for studying SGoals, and we develop
kernels, like sort and permutation, on such structure. Finally, we present some
popular SGoals in terms of the developed theory, we introduce sufficient
conditions for convergence of a SGoal, and we prove convergence of some popular
SGoals.

11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th