MPT_MPMIQP Multi-Parametric Mixed-Integer QP solver
sol = mpt_mpmiqp(Matrices, yalmipOptions)
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DESCRIPTION
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Solves a multi-parametric Mixed Integer QP (mpMIQP):
min 1/2 U H U + x' F U + x' Y x + Cf U + Cx x + Cc
U
s.t. G U <= W + E x
bndA*x <= bndb
where certain elements of the U vector are known to be either continuous, or
binary, or they belong to a finite alphabet.
As a solution we get n regions
sol.Pn(i) = {x : H x <= K}
with the optimizer
U = sol.Fi{i}*x + sol.Gi{i}
and the corresponding cost function expression
V(x) = x'*sol.Ai{i}*x + sol.Bi{i}*x + sol.Ci{i}
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INPUT
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Matrices - a struct with all the parameters which are needed.
See description above for explanation.
Matrices.H, Matrices.G, Matrices.W, Matrices.E, Matrices.Y,
Matrices.Cf, Matrices.Cx, Matrices.Cc
Matrices.bndA=bndA - Limits on exploration space, i.e. bndA*x<=bndb
Matrices.bndb=bndb
Matrices.vartype - Vector of {'C', 'B', 'A'} indicies.
vartype(i)='C' denotes a continuous variable
vartype(i)='B' denotes a binary variable (0/1)
vartype(i)='A' denotes a variable which can take
values from a finite alphabet
Matrices.alphabet - Matrices.alphabet{i} must contain a list of values
which the variable U(i) can take. For instance:
Matrices.vartype(2) = 'A';
Matrices.alphabet{2} = [-0.5 0 3.4];
and U(2) can only take values -0.5, 0, or 3.4
Options - additional options to pass to YALMIP:
.verbose - level of verbosity
.mp.algorithm - which enumeration algorithm to use
(Options.mp_algorithm=3 uses different enumeration)
.mp.presolve - perform pre-solving if this option is true (default)
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OUTPUT
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"sol" structure with following fields:
Pn,Fi,Gi - for region Pn(i).H*x <= Pn(i).K computed input is
U=Fi{i}*x+Gi{i}
Pfinal - Defines the feasible state space partition (i.e. union of
all regions) as Phard.H*x<=Phard.K
Bi, Ci - cost associate to every region
see also MPT_MPLP. SOLVEMP