mosek: Solve an optimization problem

Description

Solve an optimization problem using the MOSEK Optimization Library.

Please see the 'userguide.pdf' for a detailed introduction to this package. This file is located in the "doc" directory at the root of this package: system.file("doc", "userguide.pdf", package="Rmosek")

Usage

mosek(problem, opts = list())

Arguments

problem

The optimization problem.

problem	LIST
..$sense	STRING
..$c	NUMERIC VECTOR
..$c0	NUMERIC	(OPTIONAL)
..$A	SPARSE MATRIX
..$bc	NUMERIC MATRIX (2 rows)
..$bx	NUMERIC MATRIX (2 rows)
..$cones	LIST MATRIX (2 rows)	(OPTIONAL)
..$intsub	NUMERIC VECTOR	(OPTIONAL)
..$qobj	LIST	(OPTIONAL)
..$scopt	LIST	(OPTIONAL)
..$iparam/$dparam/$sparam	LIST	(OPTIONAL)
....$<MSK_PARAM>	STRING / NUMERIC	(OPTIONAL)
..$sol	LIST	(OPTIONAL)
....$itr/$bas/$int	LIST	(OPTIONAL)

opts

The interface options.

opts	LIST	(OPTIONAL)
..$verbose	NUMERIC	(OPTIONAL)
..$usesol	BOOLEAN	(OPTIONAL)
..$useparam	BOOLEAN	(OPTIONAL)
..$soldetail	NUMERIC	(OPTIONAL)
..$getinfo	BOOLEAN	(OPTIONAL)
..$writebefore	STRING (filepath)	(OPTIONAL)
..$writeafter	STRING (filepath)	(OPTIONAL)

Value

The returned results.

r	LIST
..$response	LIST
....$code	NUMERIC
....$msg	STRING
..$sol	LIST
....$itr/$bas/$int	LIST	(SOLVER DEPENDENT)
......$solsta	STRING
......$prosta	STRING
......$skc	STRING VECTOR
......$skx	STRING VECTOR
......$skn	STRING VECTOR	(NOT IN $bas)
......$xc	NUMERIC VECTOR
......$xx	NUMERIC VECTOR
......$slc	NUMERIC VECTOR	(NOT IN $int)
......$suc	NUMERIC VECTOR	(NOT IN $int)
......$slx	NUMERIC VECTOR	(NOT IN $int)
......$sux	NUMERIC VECTOR	(NOT IN $int)
......$snx	NUMERIC VECTOR	(NOT IN $int/$bas)
......$pobjval	NUMERIC	*
......$dobjval	NUMERIC	*(NOT IN $int)
......$pobjbound	NUMERIC	*($int ONLY)
......$maxinfeas	LIST	*
........$pbound	NUMERIC	*
........$peq	NUMERIC	*
........$pcone	NUMERIC	*(NOT IN $bas)
........$dbound	NUMERIC	*(NOT IN $int)
........$deq	NUMERIC	*(NOT IN $int)
........$dcone	NUMERIC	*(NOT IN $int/$bas)
........$int	NUMERIC	*($int ONLY)
..$iinfo/$dinfo	LIST	*
....$<MSK_INFO>	NUMERIC	*

*Starred items must be requested using an option.

The result is a named list containing the response of the MOSEK optimization library. A response code of zero is the signal of success.

Depending on the specified solver, one or more solutions may be returned. The interior-point solution itr, the basic (corner point) solution bas, and the integer solution int.

The problem status prosta in all solutions shows the feasibility of your problem description. All solutions are described by a solution status solsta (e.g. optimal) along with the variable and constraint activities. All activities will further have a bound key that specify their value in relation to the declared bounds.

Dual variables are returned for all defined bounds wherever possible. Integer solutions int does not have any dual variables as such definitions would not make sense. Basic (corner point) solutions bas would never be returned if the problem had conic constraints, and does not define snx.

Setting option soldetail larger than 1 extracts pobjval, pobjval and pobjbound. Larger than 2 extracts maxinfeas. Setting option getinfo to TRUE extracts iinfo and dinfo. lll r Result .$response Response from the MOSEK Optimization Library ..$code ID-code of response ..$msg Human-readable message .$sol All solutions identified ..$itr/$bas/$int Solution description ...$solsta Solution status ...$prosta Problem status ...$skc Linear constraint status keys ...$skx Variable bound status keys ...$skn Conic constraint status keys ...$xc Constraint activities ...$xx Variable activities ...$slc Dual variable for constraint lower bounds ...$suc Dual variable for constraint upper bounds ...$slx Dual variable for variable lower bounds ...$sux Dual variable for variable lower bounds ...$snx Dual variable of conic constraints ...$pobjval Primal objective value ...$dobjval Dual objective value ...$pobjbound Best primal objective bound from relaxations ...$maxinfeas Maximal solution infeasibilities ....$pbound Primal inequality constraints ....$peq Primal equality constraints ....$pcone Primal cone constraints ....$dbound Dual inequality constraints ....$deq Dual equality constraints ....$dcone Dual cone constraints ....$int Integer variables .$iinfo/$dinfo MOSEK information list ..$<MSK_INFO> Value of any <MSK_INFO>

Details

The optimization problem should be described in a named list of definitions. The number of variables in the problem is determined from the number of columns in the constraint matrix A.

Like a Linear Program it has a linear objective with one coefficient in c for each variable, some optional constant c0, and the improving direction sense. Quadratic terms can be added to the objective with qobj. The constraints can either be linear, specified as rows in A with lower and upper bounds as columns in bc (you can use Inf if needed), or conic as specified in the list-typed matrix cones (add constraints copyx=x if some variable x appears in multiple cones). All variables have lower and upper bounds as columns in bx, and will be integer if they appear in the intsub list.

As an advanced feature, non-linear unary operators involving exponential or logarithmic functions can be added with scopt. Parameters can also be specified for the MOSEK call. iparam is integer-typed parameters, dparam ia double-typed parameters and sparam is string-typed parameters. These parameters can be ignored by setting the option useparam to FALSE (the default is TRUE).

Initial solutions are specified in sol and should have the same format as the solution returned by the function call. This solution can be ignored by setting the option usesol to FALSE (the default is TRUE).

The amount of information printed by the interface can be limited by verbose (default=10). The generated model can be exported to any standard modeling fileformat (e.g. lp, opf, lp or mbt), with (resp. without) the identified solution using writeafter (resp. writebefore).

The optimization process can be terminated at any moment using CTRL + C.

problem	Problem description
.$sense	Objective sense, e.g. "max" or "min"
.$c	Objective coefficients
.$c0	Objective constant
.$A	Constraint matrix
.$bc	Lower and upper constraint bounds
.$bx	Lower and upper variable bounds
.$qobj	Quadratic objective terms
.$cones	Conic constraints
.$intsub	Integer variable indexes
.$scopt	Separable convex optimization
.$iparam/$dparam/$sparam	Parameter list
..$<MSK_PARAM>	Value of any <MSK_PARAM>
.$sol	Initial solution list
..$itr/$bas/$int	Initial solution description
opts	Options
.$verbose	Output logging verbosity
.$usesol	Whether to use the initial solution
.$useparam	Whether to use the specified parameter settings
.$soldetail	Level of detail used to describe solutions.
.$getinfo	Whether to extract MOSEK information items
.$writebefore	Filepath used to export model
.$writeafter	Filepath used to export model and solution

Examples

Run this code

# NOT RUN {
 lo1 <- list()
 lo1$sense <- "max"
 lo1$c <- c(3,1,5,1)
 lo1$A <- Matrix(c(3,1,2,0,
                   2,1,3,1,
                   0,2,0,3), nrow=3, byrow=TRUE, sparse=TRUE)
 lo1$bc <- rbind(blc = c(30,15,-Inf),
                 buc = c(30,Inf,25))
 lo1$bx <- rbind(blx = c(0,0,0,0),
                 bux = c(Inf,10,Inf,Inf))
 r <- mosek(lo1, list( soldetail = 1 ))
# }