MOSEK Optimization Suite

Warnings

• breaking MOSEK is commercial software and requires a valid license to function. Even after `pip install mosek`, you must obtain and configure a license file (e.g., `mosek.lic`) by placing it in a default location or setting the `MOSEKLM_LICENSE_FILE` environment variable. Without a license, optimization calls will fail.
  Fix: Obtain a trial, academic, or commercial license from mosek.com and follow the licensing guide to place the `mosek.lic` file or set the `MOSEKLM_LICENSE_FILE` environment variable.
• breaking Upgrading to a new major version (e.g., from MOSEK 10 to 11) can introduce API incompatibilities and changes in default parameter behaviors. Users who have tuned solver parameters are recommended to re-evaluate their settings.
  Fix: Consult the release notes and interface changes section in the documentation for the specific major version upgrade. Re-evaluate any custom solver parameter settings.
• deprecated In the Optimizer API, conic constraints restricted to `x ∈ K` for a variable `x` are deprecated and will be removed in a future major version.
  Fix: Migrate to using affine conic constraints instead.
• deprecated The MOSEK conda package is deprecated and may be dropped in a future release.
  Fix: Prefer `pip install mosek` for Python API installation.
• gotcha Repeatedly creating and destroying `mosek.Env()` or `mosek.fusion.Model` objects for many small optimization problems can incur significant performance overhead due to the license checkout system.
  Fix: Reuse the MOSEK environment (or `mosek.fusion.Model` object) for multiple optimizations where possible, as the license token remains checked out within the environment's lifetime. Set `cacheLicense` to 'off' or `Model.putlicensewait` if specific license management is needed.
• gotcha Using the Fusion API, assigning names to all variables, constraints, and other model elements can substantially increase problem setup time. This overhead should be avoided in time-critical applications.
  Fix: Avoid assigning names to model elements if setup time is critical for performance. Names are primarily for debugging and readability.
• gotcha Passing NumPy arrays of incorrect integer types (e.g., `int64` where `int32` is expected, or vice versa) to the MOSEK API will trigger warnings and cause the module to make internal copies, potentially impacting performance.
  Fix: Ensure that NumPy arrays passed to the MOSEK API have the expected integer data types (typically `int32` for indices, `float64` for numerical data) to avoid unnecessary internal data conversions.

Install

• pip install mosek Install Python API

Imports

• mosek

  import mosek

  For the Optimizer API, or to access general MOSEK constants and environment.
• fusion

  import mosek.fusion as msk

  For the object-oriented Fusion API. The 'pythonic' submodule provides convenience operators.

Quickstart

This quickstart demonstrates a basic Linear Programming (LP) problem using MOSEK's Optimizer API. It initializes a MOSEK environment and task, defines variables and constraints, sets the objective, solves the problem, and retrieves the solution. A MOSEK license is required to run this code; ensure your license file is correctly configured, typically via the `MOSEKLM_LICENSE_FILE` environment variable or by placing `mosek.lic` in `~/.mosek/` (or `%USERPROFILE%\mosek\` on Windows).

import mosek
import os

# Configure MOSEK license path. Replace 'path/to/your/mosek.lic' with actual path.
# For academic/trial licenses, it often defaults to ~/.mosek/mosek.lic
# It's recommended to set MOSEKLM_LICENSE_FILE environment variable for production.
# For quickstart, ensure the license file is accessible or MOSEKLM_LICENSE_FILE is set.
# os.environ['MOSEKLM_LICENSE_FILE'] = os.environ.get('MOSEKLM_LICENSE_FILE', 'path/to/your/mosek.lic')

# Define a stream printer to capture MOSEK output (optional)
def streamprinter(text):
    # print(text.strip())
    pass

try:
    # Create a MOSEK environment
    with mosek.Env() as env:
        # Attach a stream printer to the environment
        env.set_Stream(mosek.streamtype.log, streamprinter)

        # Create a task for optimization
        with env.Task() as task:
            task.set_Stream(mosek.streamtype.log, streamprinter)

            # Problem: Minimize x + y subject to x >= 0, y >= 0, x + y >= 1

            # Append two variables
            task.appendvars(2)
            # Set variable bounds to be free initially
            task.putvarboundlist([0, 1], [mosek.boundkey.fr, mosek.boundkey.fr], [0.0, 0.0], [0.0, 0.0])

            # Append one constraint
            task.appendcons(1)
            # Set constraint bound (x + y >= 1)
            task.putconbound(0, mosek.boundkey.lo, 1.0, 1.0)

            # Set coefficients for constraint (x + y)
            task.putaij(0, 0, 1.0) # Constraint 0, Variable 0, Coefficient 1.0
            task.putaij(0, 1, 1.0) # Constraint 0, Variable 1, Coefficient 1.0

            # Set objective coefficients (Minimize x + y)
            task.putclist([0, 1], [1.0, 1.0])
            # Set objective sense to minimize
            task.putobjsense(mosek.objsense.minimize)

            # Solve the problem
            task.optimize()
            task.solutionsummary(mosek.streamtype.log)

            # Get and print the solution
            prosta = task.getprosta(mosek.soltype.itr)
            if prosta == mosek.prosta.prim_feas_obj_and_dual_feas_obj:
                xx = [0.0] * 2
                task.getxx(mosek.soltype.itr, xx)
                print(f"Solution: x = {xx[0]}, y = {xx[1]}")
            else:
                print("Problem status: ", prosta)

except mosek.Error as e:
    print(f"MOSEK Error: {e.code} {e.msg}")
except Exception as e:
    print(f"General Error: {e}")