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.
`mipstructs`	Struct vector defining additional MIP constraints. The number of MIP structs is given by the number of elements in the struct. Each struct must have mipstructs(i).type, which defines the constraint type and the remainder of the struct:
	`mipstructs(i).type='1'` or `'2'`		These define SOS1 or SOS2 constraints, in this case the struct needs to define the following additional vectors:
		`mipstructs(i).ind`	numeric vector with the indices of columns in the set (column indices start from 0);
		`mipstructs(i).wt`	numeric vector with the reference row weights corresponding to the columns in the `mipstructs(i).ind` vector. It must have the same length as `mipstructs(i).ind`.
	`mipstructs(i).type='i'`		This declares one of the rows in the constraint matrix as an indicator constraint. In this case the following additional entries are required:
		`mipstructs(i).row`	0-based index of a row in the `A`-matrix that should be changed to an indicator;
		`mipstructs(i).col`	0-based index of the binary indicator variable that should activate the constraint;
		`mipstructs(i).comp`	Either `+1` if the row should be active if the variable takes value one or `-1` if the row should be active if the binary takes value zero.
	`mipstructs(i).type='p'`		This declares a piecewise linear constraint `y = f(x)` and requires the following additional arguments:
		`mipstructs(i).res`	0-based index of the resulting column `y`;
		`mipstructs(i).col`	0-based index of the input column `x`;
		`mipstructs(i).x`	numeric vector with `x`-coordinates of breakpoints that define function `f` (for more details please refer to the C documentation);
		`mipstructs(i).y`	numeric vector with `y`-coordinates of breakpoints.
	`mipstructs(i).type='n'` or `'x'` or `'d'` or `'r'` or `'s'`		This declares a miN, maX, anD, oR or abS general constraint (like `y = max (x_i)`) with the following additional struct members:
		`mipstructs(i).res`	0-based index of the resulting column `y`;
		`mipstructs(i).cols`	numeric vector with the indices of the input columns `x_i` (column indices start from 0); for `abs` this has to be a single index;
		`mipstructs(i).vals`	numeric vector of constants to include in the `min`/`max` (ignored for `and`/`or`/`abs`).
`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