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# xprsqcqp

Purpose
Solve quadratically constrained quadratic programming problems with Xpress.
Synopsis
`x = xprsqcqp(H,f,A,Q,b,rtype,lb,ub,options)`
`[x,fval,exitflag,output,lambda] = xprsqcqp(...)`
Input arguments

H | Matrix for quadratic objective terms
f | Linear objective function vector
A | Matrix for the linear part of the constraints
Q | 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 [].
b | Vector for constraints RHS
rtype | Character vector (string) giving the row types:
L | indicates a ≤ row
E | indicates a = row
G | indicates a ≥ row
N | indicates a free row
If rtype = [], all rows are assumed to be of type 'L'. If rtype is a single character, all constraints are assigned the corresponding type.
lb | Lower bounds. If lb = [] it means there are no lower bounds. If lb is a scalar, x is uniformly bounded by that scalar.
ub | Upper bounds. If ub = [] it means there are no upper bounds. If ub is a scalar, x is uniformly bounded by that scalar.
options | Options structure created with optimset or xprsoptimset functions. See xprsoptimset for more details.

Output arguments

x | 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.
fval | Value of the objective function at the solution x.
exitflag | Integer identifying the reason the optimization algorithm terminated. The following lists the values of exitflag and the corresponding reasons the algorithm terminated.
1 | function converged to a solution x (LPSTATUS=OPTIMAL)
0 | number of iterations exceeded iter limit (LPSTATUS=UNFINISHED and STOPSTATUS=ITERLIMIT)
-2 | no feasible point was found (LPSTATUS=INFEAS)
-3 | problem is unbounded (LPSTATUS=UNBOUNDED)
-8 | other stop reason, see LPSTATUS and STOPSTATUS for details
output | 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.
lambda | Structure containing the Lagrange multipliers at the solution x (separated by constraint type). The fields of the structure are:
lower | lower bounds lb
upper | upper bounds ub
lin | linear constraints from matrix A

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.
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
xprsoptimset, quadprog
Parent Topic Xpress MATLAB functions

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