Download TOMLAB /MINLP manual - TOMLAB Optimization

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TOMLAB /MINLP Solver Reference
The MINLP solvers are a set of Fortran solvers that were developed by Roger Fletcher and Sven Leyffer, University of Dundee, Scotland. All solvers are available for sparse and dense continuous and mixed-integer quadratic
programming (qp,miqp) and continuous and mixed-integer nonlinear constrained optimization.
Table 2 lists the solvers included in TOMLAB /MINLP. The solvers are called using a set of MEX-file interfaces
developed as part of TOMLAB. All functionality of the MINLP solvers are available and changeable in the
TOMLAB framework in Matlab.
Detailed descriptions of the TOMLAB /MINLP solvers are given in the following sections. Extensive TOMLAB
m-file help is also available, for example help minlpBBTL in Matlab will display the features of the minlpBB solver
using the TOMLAB format.
TOMLAB /MINLP package solves mixed-integer nonlinear programming (minlp) problem defined as
min f (x)
x
−∞ <
s/t
xL
bL
cL
≤
x
≤ xU < ∞
≤ Ax ≤ bU
≤ c(x) ≤ cU , xj ∈ N
(1)
∀j ∈I,
where x, xL , xU ∈ Rn , f (x) ∈ R, A ∈ Rm1 ×n , bL , bU ∈ Rm1 and cL , c(x), cU ∈ Rm2 . The variables x ∈ I, the index
subset of 1, ..., n, are restricted to be integers.
mixed-integer quadratic programming (miqp) problems defined as
min f (x) = 21 xT F x + cT x
x
s/t
xL
bL
≤ x ≤ xU ,
≤ Ax ≤ bU
(2)
where c, x, xL , xU ∈ Rn , F ∈ Rn×n , A ∈ Rm1 ×n , and bL , bU ∈ Rm1 . The variables x ∈ I, the index subset of
1, ..., n, are restricted to be integers.
as well as sub-types of these problems.
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