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edited May 27 at 11:33

Edit: The following code passes without errors. However, contrary to Erling's mention below, dualization was not needed. Is this a correct implementation?

from mosek.fusion import *
import mosek.fusion.pythonic
import numpy as np

# Define the dimensions
n = 4
p = 3
m = 2
q = 2

# Generate random fixed data for the problem
np.random.seed()
E = np.random.randn(n, p)
A = np.random.randn(p, p)
A = (A + A.T) / 2  # Make A symmetric
B = np.random.randn(p, p)
B = (B + B.T) / 2  # Make B symmetric
F = np.random.randn(q, m)
a = np.random.randn(q)
b = np.random.randn(q)

# Create a new model
with Model("example") as M:
    # Define the variables
    X = M.variable("X", Domain.inPSDCone(n))
    x = M.variable("x", m, Domain.unbounded())
    nu = M.variable("nu", 1, Domain.unbounded())
    lam = M.variable("lambda", 1, Domain.greaterThan(0.0))

    # PSD constraint: E^T X E + lambda * A + nu * B >= 0
    M.constraint("psd_constraint", E.T @ X @ E + lam[0] * A + nu[0] * B, Domain.inPSDCone())

    # Linear equality constraint: Fx + lambda * a + nu * b = 0
    M.constraint("linear_constraint", F @ x + lam[0] * a + nu[0] * b, Domain.equalsTo(0.0))

    # Solve the problem
    M.solve()
    
    # Retrieve and print the solution
    X_sol = X.level()
    x_sol = x.level()
    nu_sol = nu.level()
    lam_sol = lam.level()
    
    print("Solution X:\n", np.array(X_sol).reshape((n, n)))
    print("Solution x:", x_sol)
    print("Solution nu:",nu_sol[0])
    print("Solution lambda:", lam_sol[0])

Edit: The following code passes without errors. However, contrary to Erling's mention below, dualization was not needed. Is this a correct implementation?

from mosek.fusion import *
import mosek.fusion.pythonic
import numpy as np

# Define the dimensions
n = 4
p = 3
m = 2
q = 2

# Generate random fixed data for the problem
np.random.seed()
E = np.random.randn(n, p)
A = np.random.randn(p, p)
A = (A + A.T) / 2  # Make A symmetric
B = np.random.randn(p, p)
B = (B + B.T) / 2  # Make B symmetric
F = np.random.randn(q, m)
a = np.random.randn(q)
b = np.random.randn(q)

# Create a new model
with Model("example") as M:
    # Define the variables
    X = M.variable("X", Domain.inPSDCone(n))
    x = M.variable("x", m, Domain.unbounded())
    nu = M.variable("nu", 1, Domain.unbounded())
    lam = M.variable("lambda", 1, Domain.greaterThan(0.0))

    # PSD constraint: E^T X E + lambda * A + nu * B >= 0
    M.constraint("psd_constraint", E.T @ X @ E + lam[0] * A + nu[0] * B, Domain.inPSDCone())

    # Linear equality constraint: Fx + lambda * a + nu * b = 0
    M.constraint("linear_constraint", F @ x + lam[0] * a + nu[0] * b, Domain.equalsTo(0.0))

    # Solve the problem
    M.solve()
    
    # Retrieve and print the solution
    X_sol = X.level()
    x_sol = x.level()
    nu_sol = nu.level()
    lam_sol = lam.level()
    
    print("Solution X:\n", np.array(X_sol).reshape((n, n)))
    print("Solution x:", x_sol)
    print("Solution nu:",nu_sol[0])
    print("Solution lambda:", lam_sol[0])

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asked May 23 at 14:25

BasicUser

Minimal example using MOSEK API in python

I want to solve (simplified version) \begin{equation*} \begin{aligned} & \underset{}{\text{find}} & & X\in\mathbb{S}^{n}_{+}, x \in \mathbb{R}^{m}, \nu \in \mathbb{R}, \lambda\geq 0\\ & \text{subject to} & & E^{\top} X E + \lambda A + \nu B \succeq 0, \\ & & & Fx + \lambda a + \nu b = 0, \\ \end{aligned} \end{equation*} where \begin{align*} E &\in \mathbb{R}^{n\times p},\\ A &\in \mathbb{S}^{p}, \\ B &\in \mathbb{S}^{p}, \\ F &\in \mathbb{R}^{q \times m}, \\ a &\in \mathbb{R}^{q}, \\ b &\in \mathbb{R}^{q} \end{align*} are fixed.

I use Python with CVXPY and the MOSEK solver, which I find unreliable. Matlab with CVX and MOSEK is more reliable. I recently found that there is a MOSEK API for Python. However, the tutorial page does not directly cover this use case. I'm looking for a minimal example covering this case.