13.2 Linear/Simplex Toolbox API

Reference for moseklinmodel, the API for defining and solving linear problems. Most linear problems can be solved using the main entry point mosekmodel. This part of the API is intended primarily for users who need to use the simplex algorithm and its associated features: basic solution and warm-start.

For tutorials with explanations and full code examples see Sec. 7 (Optimization Tutorials), and especially Sec. 7.7 (The linear/simplex interface tutorial).

13.2.1 Construction

model = moseklinmodel(name, numvar, objsense, objective, objfixterm, A, b, blx, bux, solution_x, solution_y, solution_slx, solution_sux, solution_skc, solution_skx, varnames, connames)

Creates a model, which represents a linear problem. Most of the problem’s data can be set directly in this constructor; problem data can also be input and altered using dedicated methods later. The model object is the user’s access point to the problem and solution.

Return:

model (moseklinmodel) – The created linear model object.

Parameters:

  • name (string) – (optional) Name of the model.

  • numvar (uint32) – (optional) Number of scalar variables initially in the model.

  • objsense (string) – (optional) Objective sense: "min", "minimize", "max", "maximize".

  • objective (double(:,1)) – (optional) Objective vector of length matching numvar, if provided.

  • objfixterm (double) – (optional) Fixed term in the objective.

  • A (double(:,:)) – (optional) The linear constraint matrix.

  • b (double(:,1)) – (optional) The linear constraint right-hand side.

  • blx (double(:,1)) – (optional) Variable lower bounds.

  • bux (double(:,1)) – (optional) Variable upper bounds.

  • solution_x (double(:,1)) – (optional) Initial x solution, primal solution values.

  • solution_y (double(:,1)) – (optional) Initial y solution, dual values of linear constraints.

  • solution_slx (double(:,1)) – (optional) Initial slx solution, dual values of variable lower bounds.

  • solution_sux (double(:,1)) – (optional) Initial sux solution, dual values of variable upper bounds.

  • solution_skc (string(:,1)) – (optional) Initial skc solution, status keys of constraints.

  • solution_skx (string(:,1)) – (optional) Initial skx solution, status keys of variables.

  • varnames (string(:,1)) – (optional) Names of variables.

  • connames (string(:,1)) – (optional) Names of constraints.

Example:

model = moseklinmodel(...
              name = "lo1", ...
              numvar = 6, ...
              objsense = "maximize", ...
              objective = [ 3 1 5 1 0 0 ]', ...
              A = [ 3 1 2 0  0  0 ; ...
                    2 1 3 1 -1  0 ; ...
                    0 2 0 3  0 -1 ], ...
              b = [ 30 15 25 ]', ...
              blx = [ 0.0  0.0 0.0 0.0   0.0 -inf ]', ...
              bux = [ inf 10.0 inf inf   inf  0.0 ]')

13.2.2 Adding data to the model

moseklinmodel.appendcons(A, b, x, names)

Append a new constraint block of the form \(Ax=b\).

Parameters:

  • A (double(:,:)) – (required) Matrix block of the appended constraints.

  • b (double(:,1)) – (required) Right-hand side of the constraint block. size(b,1)==size(A,1) must hold.

  • x (uint32(:,1)) – (optional) Indexes of variables. If provided, then it is assumed that the constraint blocks only involves the columns with indices in x, and size(A,2)==size(x,1) must hold.

  • names (string) – (optional) Names of the constraint rows, size(names, 1)==size(A,1) must hold.

Example:

model.appendcons([ 1 1 1 1 1 1 ], ...
                 [10]', ...
                 names = ["sum==10"])
model.appendcons(speye(6), ...
                 ones(6, 1) * 3, ...
                 names = "x_" + (1:6) + "_eq_3")
moseklinmodel.objective(objsense, objective, objfixterm)

Adds or replaces the objective in the model.

Parameters:

  • objsense (string) – (required) Objective sense: "min", "minimize", "max", "maximize".

  • objective (double(:,1)) – (required) The objective vector. It’s length must match the number of variables in the model.

  • objfixterm (double(:,1)) – (optional) Fixed term in the objective;

Example:

model.objective("minimize", [4 2 0 1 1 0]')
%model.objective("maximize", sparse([1], [2], [1.5], 1, 6), objfixterm = 10.0)
moseklinmodel.setsolution(part, values)

Set an initial solution.

Parameters:

  • part (string) – (required) Indicates which part of the solution is requested: "x" for the primal variable values, "y" for dual constraint values, "slx", "sux" for duals of variable bounds, "skc", "skx" for constraint and variable status keys taken from stakey.

  • values (double(:,1)/string(,:1)) – (required) The vector of the initial solution, a double array for numerical values or a string array for status keys taken from stakey.

Example:

model.setsolution("x", [1.0 1.0 2.0 3.0 zeros(1,2)]')
model.setsolution("skx", ["low" "bas" "bas"]')
varindexes = moseklinmodel.appendvars(num, bl, bu, c, A, names)

Append num new variables.

Return:

varindexes (uint32(:,1)) – Indexes of the newly added variables.

Parameters:

  • num (double) – (required) The number of new variables.

  • bl (double(:,1)) – (optional) Lower bounds for the new variables.

  • bu (double(:,1)) – (optional) Upper bounds for the new variables.

  • c (double(:,1)) – (optional) The objective coefficients for the new variables.

  • A (double(:,:)) – (optional) Constraint matrix nonzeros for the new columns, appended horizontally to the current constraint matrix.

  • names (string(1,:)) – (optional) Names of the new variables.

Example:

model.appendvars(3, bl = [0, 0, 0], bu = [1, 1, 1], ...
                 names = "tmp_" + (1:3))
model.appendvars(1, bl = [-1], bu = [1], ...
                 A = sparse([2 zeros(1,9)]'), c = [1]', ...
                 names = ["slack"])

13.2.3 Solving and obtaining the solution

moseklinmodel.solve(write_to_file, logfile, nosolve, quiet, optserver, analyze, licfile, liccode, param)

Invokes the optimizer to solve the problem.

Parameters:

  • write_to_file (string) – (optional) Write the problem to this file before solving. The extension specifies the file format.

  • logfile (string) – (optional) Write log to this file.

  • nosolve (logical) – (optional) Format and load problem, but do not solve.

  • quiet (logical) – (optional) Do not print log.

  • optserver (string) – (optional) Host name for remote optimization.

  • licfile (string) – (optional) License file path. The same value must be used in all calls in the current process, otherwise the outcome is undefined.

  • liccode (char(1,:)) – (optional) License key as string. The same value must be used in all calls in the current process, otherwise the outcome is undefined.

  • analyze (logical) – (optional) Whether to run the problem analyzer after optimization.

  • param (string(1,:)) – (optional) Array of parameters in the form [name, value, name, value,...].

Example:

model.solve()
model.solve(quiet = true)
model.solve(quiet = true, param = ["MSK_DPAR_OPTIMIZER_MAX_TIME", "10.0"])
exists, prosta, solsta = moseklinmodel.hassolution()

Check if the basic solution exists and return its statuses.

Return:

  • exists (logical) – Indicates if the basic solution is available.

  • prosta (string) – (optional) A string indicating the problem status for the basic solution, one of prosta. Only returned if exists is true.

  • solsta (string) – (optional) A string indicating the solution status for the basic solution, one of solsta. Only returned if exists is true.

Example:

[exists, prosta, solsta] = model.hassolution()
value, prosta, solsta = moseklinmodel.getsolution(part)

Return the requested solution values for the basic solution. Throws an error if the basic solution is not available; use moseklinmodel.hassolution to check solution availability.

Return:

  • value (double(:,1)/string(:,1)) – The solution values requested. Returns a double array for numerical values and string array for status keys.

  • prosta (string) – A string indicating the problem status for the basic solution, one of prosta.

  • solsta (string) – A string indicating the solution status for the basic solution, one of solsta.

Parameters:

part (string) – (required) Indicates which part of the solution is requested: "x" for the primal variable values, "y" for dual constraint values, "slx", "sux" for duals of variable bounds, "skc", "skx" for constraint and variable status keys taken from stakey.

Example:

x = model.getsolution("x")
y = model.getsolution("y")
skc = model.getsolution("skc")

13.2.4 Modifying the model

moseklinmodel.setb(b, first)

Update the constraint right-hand side vector b or its slice.

Parameters:

  • b (double(:,1)) – (required) New sequence of values.

  • first (int32) – (optional) The first index of the slice to be updated. Default equals to 1.

Example:

model.setb([3, 4, 5]', first = 2)
moseklinmodel.setvarbounds(bl, bu, first)

Update the variable bounds for all variables or their slice.

Parameters:

  • bl (double(:,1)) – (optional) New sequence of lower bounds.

  • bu (double(:,1)) – (optional) New sequence of upper bounds.

  • first (int32) – (optional) The first index of the slice to be updated. Default equals to 1.

Example:

model.setvarbounds(bl = [5], bu = [6], first = 5)
moseklinmodel.setrows(A, first)

Update a slice of rows in the constraint matrix A.

Parameters:

  • A (double(:,:)) – (required) A matrix of new row values. The second dimension size(A,2) must equal the number of variables in the problem.

  • first (int32) – (optional) The first row index of the slice to be updated. Default equals to 1.

Example:

model.setrows(zeros(2, model.getnumvar()))
model.setrows(ones(1, model.getnumvar()), first = 3)
moseklinmodel.setcolumns(A, first)

Update a slice of columns in the constraint matrix A.

Parameters:

  • A (double(:,:)) – (required) A matrix of new column values. The first dimension size(A,1) must equal the number of constraints in the problem.

  • first (int32) – (optional) The first column index of the slice to be updated. Default equals to 1.

Example:

model.setcolumns(zeros(model.getnumcon(), 3))
model.setcolumns(ones(model.getnumcon(), 1), first = 3)
moseklinmodel.setc(c, first)

Update the objective vector or its slice.

Parameters:

  • c (double(:,1)) – (required) New sequence of values.

  • first (int32) – (optional) The first index of the slice to be updated. Default equals to 1.

Example:

model.setc(zeros(6, 1), first = 3)

13.2.5 Auxiliary functions

moseklinmodel.write(filename, param)

Writes the current problem to a file.

Parameters:

  • filename (string) – (required) File name to write the problem to. The format is determined by the extension.

  • param (string(1,:)) – (optional) Array of parameters in the form [name, value, name, value,...].

Example:

model.write("dump.task.gz")
model.write("save.ptf", param = ["MSK_IPAR_PTF_WRITE_SOLUTIONS", "MSK_ON"])

13.2.6 Names

moseklinmodel.varname(indexes, names)

Adds variable names to the model.

Parameters:

  • indexes (uint32(:,1)) – (required) Indexes of the variables to name.

  • names (string(:,1)) – (required) Names to assign.

Example:

model.varname(2:4, ["b", "tmp1", "tmp2"])
moseklinmodel.conname(indexes, names)

Adds constraint names to the model.

Parameters:

  • indexes (uint32(:,1)) – (required) Indexes of the constraints to name.

  • names (string(:,1)) – (required) Names to assign.

Example:

model.conname(1:2, ["cons1", "cons2"])