xprsqcqp
xprsqcqp |
Purpose
Synopsis
x = xprsqcqp(H,f,A,Q,b,rtype,lb,ub,options)
[x,fval,exitflag,output,lambda] = xprsqcqp(...)
Input arguments
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H
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Matrix for quadratic objective terms
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f
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Linear objective function vector
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A
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Matrix for the linear part of the constraints
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Q
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Cell array of length
m with the
n × n matrices for the quadratic terms of the constraints. If there is only one constraint (
m=1), then
Q can be a simple double matrix instead of a cell array. For a linear constraint, the corresponding
Q{i} matrix can be set to
[].
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b
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Vector for constraints RHS
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rtype
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Character vector (string) giving the row types:
If
rtype = [], all rows are assumed to be of type
'L'. If
rtype is a single character, all constraints are assigned the corresponding type.
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lb
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Lower bounds. If
lb = [] it means there are no lower bounds. If
lb is a scalar,
x is uniformly bounded by that scalar.
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ub
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Upper bounds. If
ub = [] it means there are no upper bounds. If
ub is a scalar,
x is uniformly bounded by that scalar.
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options
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Options structure created with
optimset or
xprsoptimset functions. See
xprsoptimset for more details.
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Output arguments
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x
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Solution found by the optimization function. If
exitflag > 0, then
x is a solution; otherwise,
x is the value of the optimization routine when it terminated prematurely.
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fval
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Value of the objective function at the solution
x.
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exitflag
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Integer identifying the reason the optimization algorithm terminated. The following lists the values of
exitflag and the corresponding reasons the algorithm terminated.
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output
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Structure containing information about the optimization and, eventually, values of Xpress controls and attributes. See
quadprog and the Section
Setting and querying controls and attributes for details.
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lambda
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Structure containing the Lagrange multipliers at the solution
x (separated by constraint type). The fields of the structure are:
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Further information
1. This routine finds the minimum of a problem specified by
min 0.5·x'·H·x + f·x
s.t. A·x + x'·Qi·x ≤|=|≥ b
lb≤ x ≤ ub
where
H is an
n × n matrix;
A is an
m × n matrix;
Q is a cell array of
n × n matrices;
f,
b,
rtype,
lb, and
ub are vectors.
s.t. A·x + x'·Qi·x ≤|=|≥ b
lb≤ x ≤ ub
2. Input arguments
rtype,
lb,
ub and
options can be omitted, with the condition that, if one is omitted, also all the following ones must be omitted (as in
x=xprsqcqp(H, f, A, Q, b, rtype)). Omitting an input argument has the same effect as passing an empty array
[].
3. All output arguments can be omitted too, again with the condition that, if one is omitted, also all the following ones must be omitted (as in
[x, fval]= xprsqcqp(H, f, A, Q, b, rtype)).
4. If the specified input bounds for a problem are inconsistent, the output
x and
fval are set to
[].
Related topics