xprsqp

Solve quadratic programming problems with Xpress Optimizer.

Syntax

x = xprsqp(H,f,A,b,rtype,lb,ub,options) [x,fval,exitflag,output,lambda] = xprsqp(...)

Description

Finds the minimum of a problem specified by

   min      0.5*x'*H*x + f*x
   st.      A*x ≤/=/≤ b
            lb ≤ x ≤ ub

H is an n x n matrix; A is an m x n matrix; f, b, rtype, lb, and ub are vectors.

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=xprsqp(H,f,A,b,rtype)). Omitting an input argument has the same effect as passing an empty array [].

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]=xprsqp(H,f,A,b,rtype)).

Note If the specified input bounds for a problem are inconsistent, the output x and fval are set to [].

Input Arguments

`H`	Matrix for quadratic objective terms.
`f`	Linear objective function vector.
`A`	Matrix for linear constraints.
`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 uniformely bounded by that scalar.
`ub`	Upper bounds. If `ub` = `[]` it means there are no upper bounds. If `ub` is a scalar, `x` is uniformely 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=UNDOUNDED).
	`-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`

xprsqp

Syntax

Description

Input Arguments

Output Arguments

See Also