class_docstr: Barrier optimization problem:
      minimize fun(x) - barrier_parameter*sum(log(s))
      subject to: constr_eq(x)     = 0
                constr_ineq(x) + s = 0
docstr: Returns Lagrangian Hessian (in relation to `x`) -> Hx
docstr_tok: ["Returns","Lagrangian","Hessian","(","in","relation","to","`","x","`",")","-",">","Hx"]
code: def lagrangian_hessian_x(self, z, v):
      """Returns Lagrangian Hessian (in relation to `x`) -> Hx"""
      x = self.get_variables(z)
      # Get lagrange multipliers related to nonlinear equality constraints
      v_eq = v[: self.n_eq]
      # Get lagrange multipliers related to nonlinear ineq. constraints
      v_ineq = v[self.n_eq : self.n_eq + self.n_ineq]
      lagr_hess = self.lagr_hess
      return lagr_hess(x, v_eq, v_ineq)
  
imports: import scipy.sparse
  import numpy
  from .equality_constrained_sqp import equality_constrained_sqp
  from scipy.sparse.linalg import LinearOperator
label_desc: Use image node_id 13 for calling the BarrierSubproblem obj's underlying member method code with example usage: obj.lagrangian_hessian_x(z, v) and returns: lagr_hess