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mosek_io

mosek_io#

class MosekProblem(domain: Mesh, name: str)[source]#

A generic optimization problem using the Mosek optimization solver.

Parameters:

  • domain (dolfinx.mesh.Mesh) – Underlying mesh.

  • name (str) – Problem name.

add_convex_term(conv_fun: ConvexTerm)[source]#

Add the convex term conv_fun to the problem.

add_eq_constraint(A=None, b=0.0, bc=None, name=None)[source]#

Add a linear equality constraint \(Ax = b\).

The constraint matrix A is expressed through a linear form involving optimization variables and Lagrange multiplier test functions. The right-hand side is a linear form involving the same Lagrange multiplier. Naming the constraint enables to retrieve the corresponding Lagrange multiplier optimal value.

Parameters:

  • A (Form) – A linear form involving optimization variables. If A contains constant terms, the latter are transferred to the right-hand side b.

  • b (float, Form) – Right-hand side as a float or a linear form involving the same Lagrange multipliers as in A

  • bc (dolfinx.fem.dirichletbc) – boundary conditions to apply on the Lagrange multiplier (will be applied to all columns of the constraint when possible)

  • name (str) – Lagrange multiplier name

add_ineq_constraint(A=None, bl=None, bu=None, bc=None, name=None)[source]#

Add a linear inequality constraint \(b_l \leq Ax \leq b_u\).

The constraint matrix A is expressed through a linear form involving optimization variables and Lagrange multiplier test functions. The right-hand side is a linear form involving the same Lagrange multiplier. Naming the constraint enables to retrieve the corresponding Lagrange multiplier optimal value.

Parameters:

  • A (Form) – A linear form involving optimization variables. If A contains constant terms, the latter are transferred to the right-hand side b.

  • bl (float, Form) – Lower-bound as a float or a linear form involving the same Lagrange multipliers as in A

  • bu (float, Form) – Same as bl.

  • bc (dolfinx.fem.dirichletbc) – boundary conditions to apply on the Lagrange multiplier (will be applied to all columns of the constraint when possible)

  • name (str) – Lagrange multiplier name

add_obj_func(obj)[source]#

Add an objective function.

Parameters:

obj (linear form)

add_var(V, cone=None, lx=None, ux=None, bc=None, name=None)[source]#

Add a (list of) optimization variable.

The added variables belong to the corresponding FunctionSpace V.

Parameters:

  • V ((list of) FunctionSpace) – variable FunctionSpace

  • cone ((list of) Cone) – cone in which each variable belongs (None if no constraint)

  • ux ((list of) float, Function) – upper bound on variable \(x \leq u_x\)

  • lx ((list of) float, Function) – lower bound on variable \(l_x \leq x\)

  • bc ((list of) DirichletBC) – boundary conditions applied to the variables (None if no bcs)

  • name ((list of) str) – name of the associated functions

Returns:

x – optimization variables

Return type:

Function tuple

get_dual_var(var)[source]#

Retrieves dual variable function associated with var.

get_lagrange_multiplier(name)[source]#

Retrieves Lagrange multiplier function associated with constraint name.

get_solution_info(output=True)[source]#

Return information dictionary on the solution.

If output=True, it gets printed out.

optimize(sense='min', dump=False)[source]#

Write the problem in Mosek format and solves.

Parameters:

  • sense ({"min[imize]", "max[imize]"}) – sense of optimization

  • dump (bool) – dumps the problem to a .ptf file format, default=False

Returns:

  • pobj (float) – the computed primal optimal value

  • dobj (float) – the computed dual optimal value

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