Dual formulation of the minimal sphere enclosing points using MOSEK Fusion API

gistfile1.py

def sphere_enclosing_dual(n,k,p):
    print('Creating the Fusion optimization model...')

    start=time.clock()
    M = Model("minimal sphere enclosing a set of points dual")
    

    print('Declaring the variables...')
    y= M.variable('y',NDSet(k,n+1),Domain.inQCone(k,n+1))
    print('done!\n')

    c=[0. for i in range(n+1)]
    c[0]=1.


    print('Defining the constraints...')
    M.constraint('lin', Expr.mul(DenseMatrix(1,k,1.0), y), Domain.equalsTo(c) )
    print('done!\n')

  
    print('Defining the objective function...')
    M.objective('dual',ObjectiveSense.Maximize, Expr.sum(Expr.mulDiag(\
                                                                      DenseMatrix(p.tolist()),\
                                                                      y.slice([0,1],[k,n+1]).transpose())))
                                                                      
    print('done!\n')
 
    print('Model building time: '+ str(time.clock()-start))
    M.setLogHandler(sys.stdout)
    M.solve()
    print("\nSolution status= "+ str(M.getPrimalSolutionStatus()))