"MOSEK" (Optimization Method)


  • MOSEK is a commercial solver for large-scale sparse linear and quadratic optimization problems with real and mixed-integer variables and conic optimization problems with real variables.
  • In addition to real-valued conic problems, MOSEK allows mixed-integer variables in combination with the linear, quadratic, exponential and power cones.
  • Visit the following page for information on how to get a license from MOSEK ApS.
  • Method"MOSEK" can be used in any convex optimization function as well as NMinimize and related functions for appropriate problems.
  • Possible options for method "MOSEK" and their corresponding default values are:
  • MaxIterationsAutomaticmaximum number of iterations to use
    ToleranceAutomaticthe tolerance to use for internal comparisons
    MethodAutomaticMOSEK submethod


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Basic Examples  (2)

Minimize subject to the constraint with method "MOSEK":

Minimize TemplateBox[{{{, {x, ,, y}, }}}, Norm] subject to the constraints , for integer with method "MOSEK":

Scope  (17)

Applicable Functions  (8)

Use NMaximize with method "MOSEK" to maximize 1-TemplateBox[{{x, +, {2, y}}}, Abs] subject to linear constraints:

Use ConvexOptimization to minimize over a disk centered at with radius

Get the minimum value and the minimizing vector using solution properties:

Use ConicOptimization to minimize subject to TemplateBox[{{x, +,  , y}}, Abs]^(1.5)<=t and {x,y} in Disk[{1,1}]:

Get the dual maximizer:

Use SemidefiniteOptimization to minimize subject to the positive semidefinite matrix constraint (x 1; 1 y)_(TemplateBox[{2}, SemidefiniteConeList])0:

Find the solution:

Use SecondOrderConeOptimization to minimize subject to :

Define the objective as and the constraints as TemplateBox[{{{{a, _, i}, ., x}, +, {b, _, i}}}, Norm]<=alpha_i.x+beta_i,i=1,2:

Specify the equality constraint as:

Solve using matrix-vector inputs:

Use QuadraticOptimization to minimize minimize subject to and :

Define objective as and constraints as and :

Solve using matrix-vector inputs:

Use LinearOptimization to minimize subject to :

Combine the coefficients into and use a vector variable :

Use GeometricOptimization to maximize the area of a rectangle such that the perimeter is at most 1:

Scalable Problems  (9)

Minimize Total[x] subject to the constraint using vector variable with non-negative values:

Minimize Total[x] subject to the constraint with a non-negative integer-valued vector:

Minimize Total[x] subject to the constraint using a vector variable :

Minimize the sum of the integer-valued coordinates of a point lying within a 1000-dimensional unit ball:

Minimize for a sparse symmetric semidefinite matrix , subject to constraint :

Minimize subject to the constraint for large sparse matrices , and :

Minimize x.Q.x+Total[x] for a sparse symmetric semidefinite matrix , subject to Total[x]1:

Given an matrix with non-negative real entries, find a diagonal matrix with positive entries that minimizes the sum of squares (the Frobenius norm squared) of the similar matrix :

Let be the diagonal entries of . Since is positive, the entries of are , so the entries of the product are :

Find that minimizes :