xprsmiqp

Solve mixed integer quadratic programming problems with Xpress Optimizer.

Syntax

x = xprsmiqp(H,f,A,b,rtype,ctype,clim,sos,lb,ub,x0,options) [x,fval,exitflag,output] = xprsmiqp(...)

Description

Finds the minimum of a problem specified by

   min      0.5*x'*H*x + f*x
   st.      A*x ≤/=/≤ b
            lb ≤ x ≤ ub
            x in the domain specified by the ctype, clim and SOS arguments

H is an n x n matrix; A is an m x n matrix; f, b, rtype, ctype, clim, lb, ub and x0 are vectors; sos is a struct vector.

Input arguments rtype and followings can be omitted, with the condition that, if one is omitted, also all the following ones must be omitted (as in x=xprsmiqp(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]=xprsmiqp(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.
`ctype`	Character vector (string) giving the column types: `C` or `\0` continuous variables; `B` binary variables; `I` integer variables; `P` partial integer variables; `S` semi-continuous variables; `R` semi-continuous integers. If `ctype` = `[]`, all columns are assumed to be of type `C`. If `ctype` is a single character, all columns are assigned the corresponding type.
`clim`	Vector containing the integer limits for the partial integer variables and lower bounds for semi-continuous and semi-continuous integer variables (column types `P`, `S`, `R`). Values in the positions corresponding to all other columns are ignored. `clim` is mandatory if there are any `P`, `S` or `R` columns. If `clim` is a scalar, all columns are assigned to that same limit.
`sos`	Struct vector defining SOS sets. The number of SOS sets is given by the number of elements in the struct. The struct must contain the following fields:
	`sos(i).type`	a character indicating the SOS type, either `'1'` or `'2'`;
	`sos(i).ind`	numeric vector with the indices of columns in the set (column indices start from 0);
	`sos(i).wt`	numeric vector with the reference row weights corresponding to the columns in the `sos(i).ind` vector. It must have the same length as `sos(i).ind`.
`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.
`x0`	Optional initial known solution used to speed-up search.
`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` (MIPSTATUS=MIP_OPTIMAL).
	`0`	Number of iterations exceeded iter limit (STOPSTATUS=ITERLIMIT).
	`-2`	The problem is infeasible (MIPSTATUS=MIP_INFEAS).
	`-4`	Number of searched nodes exceeded limit (STOPSTATUS=STOP_NODELIMIT).
	`-5`	Search time exceeded limit (STOPSTATUS=STOP_TIMELIMIT).
	`-8`	Other stop reason, see `MIPSTATUS` and `STOPSTATUS` for details.
`output`	Structure containing information about the optimization and, eventually, values of Xpress controls and attributes. See `bintprog` and the section Setting and querying controls and attributes for details.

xprsmiqp

Syntax

Description

Input Arguments

Output Arguments

See Also