Problem Interface

Having built a problem, PyCUTEst returns an instance of class CUTEstProblem (for fixed variables, its behaviour can be set with the drop_fixed_variables flag for import_problem()).

Problem Methods

The methods available for each CUTEstProblem instance are:

• obj(x[, gradient]): evaluate objective (and optionally its gradient)

• grad(x[, index]): evaluate objective gradient or specific constraint gradient

• objcons(x): evaluate objective and constraints

• cons(x[, index, gradient]): evaluate constraint(s) and optionally their Jacobian/its gradient

• lag(x, v[, gradient]): evaluate Lagrangian function value and optionally its gradient

• lagjac(x[, v]): evaluate gradient of objective/Lagrangian and Jacobian of constraints

• jprod(p[, transpose, x]): evaluate constraint Jacobian-vector product

• hess(x[, v]): evaluate Hessian of objective or Lagrangian

• ihess(x[, cons_index]): evaluate Hessian of objective or a specific constraint

• hprod(p[, x, v]): evaluate Hessian-vector product (for objective or Lagrangian)

• gradhess(x[, v, gradient_of_lagrangian]): evaluate gradient of objective/Lagrangian, Jacobian of constraints and Hessian of objective/Lagrangian

• report(): return a dictionary of statistics (number of objective/gradient evaluations, etc.)

For large-scale problems, you may want to get vectors/matrices as sparse matrices. We have the following methods which return sparse matrices:

• sobj(x[, gradient]): (sparse) evaluate objective (and optionally its gradient)

• sgrad(x[, index]): (sparse) evaluate objective gradient or specific constraint gradient

• scons(x[, index, gradient]): (sparse) evaluate constraint(s) and optionally their Jacobian/its gradient

• slagjac(x[, v]): (sparse) evaluate gradient of objective/Lagrangian and Jacobian of constraints

• sphess(x[, v]): (sparse) evaluate Hessian of objective or Lagrangian

• isphess(x[, cons_index]): (sparse) evaluate Hessian of objective or a specific constraint

• gradsphess(x[, v, gradient_of_lagrangian]): (sparse) evaluate gradient of objective/Lagrangian, Jacobian of constraints and Hessian of objective/Lagrangian

Full documentation for each method above is given by clicking on it.

Problem Attributes

Each CUTEstProblem instance has the following attributes:

• name: CUTEst problem name (string)

• n: number of variables (equal to n_free if drop_fixed_variables=True, otherwise n_full)

• m: number of constraints

• x0: starting point for optimization routine (NumPy array of shape (n,))

• sifParams: dict of parameters passed to sifdecode

• sifOptions: list of extra options passed to sifdecode

• vartype: array of variable types (NumPy array size n, entry vartype[i] indicates that x[i] is real(0), boolean(1), or integer(2))

• nnzh: number of nonzero entries in upper triangular part of objective Hessian (for all variables, including fixed)

• nonlinear_vars_first: flag if all nonlinear variables are listed before linear variables

• bl: array of lower bounds on input (unconstrained -> -1e20), as NumPy array of shape (n,)

• bu: array of upper bounds on input (unconstrained -> 1e20), as NumPy array of shape (n,)

• n_full: total number of variables in CUTEst problem (n_free + n_fixed)

• n_free: number of free variables

• n_fixed: number of fixed variables

For constrained problems, we also have (these are all set to None for unconstrained problems):

• eq_cons_first: flag if equality constraints are listed before inequality constraints

• linear_cons_first: flag if linear constraints are listed before nonlinear constraints

• nnzj: number of nonzero entries in constraint Jacobian (for all variables, including fixed)

• v0: starting point for Lagrange multipliers (NumPy array of shape (m,))

• cl: lower bounds on constraints, as NumPy array of shape (m,)

• cu: upper bounds on constraints, as NumPy array of shape (m,)

• is_eq_cons: NumPy array of Boolean flags indicating if i-th constraint is equality or not (i.e. inequality)

• is_linear_cons: NumPy array of Boolean flags indicating if i-th constraint is linear or not (i.e. nonlinear)

Full method documentation

Please click on a CUTEstProblem method below for full documentation:

obj(x[, gradient])	Evaluate the objective (and optionally its gradient).
grad(x[, index])	Evaluate the gradient of the objective function or gradient of the i-th constraint.
objcons(x)	Evaluate objective and constraints.
cons(x[, index, gradient])	Evaluate the constraints (and optionally their Jacobian or gradient).
lag(x, v[, gradient])	Evaluate Lagrangian function value and its gradient if requested.
lagjac(x[, v])	Evaluate gradient of objective or Lagrangian, and Jacobian of constraints.
jprod(p[, transpose, x])	Evaluate product of constraint Jacobian with a vector p
hess(x[, v])	Evaluate the Hessian of the objective or Lagrangian.
ihess(x[, cons_index])	Evaluate the Hessian of the objective or the i-th constraint.
hprod(p[, x, v])	Calculate Hessian-vector product H*p, where H is Hessian of objective (unconstrained) or Lagrangian (constrained).
gradhess(x[, v, gradient_of_lagrangian])	Evaluate the gradient of objective or Lagrangian, Jacobian of constraints, and Hessian of objective or Lagrangian.
report()	Get CUTEst usage statistics.
sobj(x[, gradient])	Evaluate the objective (and optionally its sparse gradient).
sgrad(x[, index])	Evaluate the sparse gradient of the objective function or sparse gradient of the i-th constraint.
scons(x[, index, gradient])	Evaluate the constraints (and optionally their sparse Jacobian or gradient).
slagjac(x[, v])	Evaluate sparse gradient of objective or Lagrangian, and sparse Jacobian of constraints.
sphess(x[, v])	Evaluate sparse Hessian of objective or Lagrangian.
isphess(x[, cons_index])	Evaluate the sparse Hessian of the objective or the i-th constraint.
gradsphess(x[, v, gradient_of_lagrangian])	Evaluate the sparse gradient of objective or Lagrangian, sparse Jacobian of constraints, and sparse Hessian of objective or Lagrangian.