unopy 0.2.0

Uno, a highly customizable SQP & barrier solver for nonlinearly constrained optimization

Uno

Uno is a solver for nonlinearly constrained optimization that unifies Lagrange-Newton (essentially SQP and interior-point) methods. It breaks them down into a set of building blocks (e.g., strategies to compute descent directions and techniques to enforce globalization).

unopy, Uno's Python interface, allows you to solve an optimization model described by callback functions.

Example

An implementation example of the Hock-Schittkowski model hs015 is available in the file example_hs015.py.

Building an optimization model

Building an optimization model is incremental and starts with the information about the variables:

model = unopy.Model(problem_type, number_variables,
   variables_lower_bounds, variables_upper_bounds, base_indexing)

The following optional elements can be added to the model separately:

• the objective function (and its gradient). It is 0 otherwise;

model.set_objective(optimization_sense, objective_function, objective_gradient)

• constraint functions (and their Jacobian);

model.set_constraints(number_constraints, constraint_functions,
   constraints_lower_bounds, constraints_upper_bounds, number_jacobian_nonzeros,
   jacobian_row_indices, jacobian_column_indices, jacobian)

• the Lagrangian Hessian;

model.set_lagrangian_hessian(number_hessian_nonzeros, hessian_triangular_part, 
   hessian_row_indices, hessian_column_indices, lagrangian_hessian, lagrangian_sign_convention)

• a Jacobian operator (performs Jacobian-vector products);

model.set_jacobian_operator(jacobian_operator)

• a Jacobian-transposed operator (performs Jacobian-transposed-vector products);

model.set_jacobian_transposed_operator(jacobian_transposed_operator)

• a Hessian operator (performs Hessian-vector products);

model.set_lagrangian_hessian_operator(lagrangian_hessian_operator, lagrangian_sign_convention)

• user data of an arbitrary type;

model.set_user_data(user_data)

• an initial primal point;

model.set_initial_primal_iterate(initial_primal_iterate)

• an initial dual point.

model.set_initial_dual_iterate(initial_dual_iterate)

Each of these functions throws an exception upon failure.

Creating an instance of the Uno solver

Create an instance of the Uno solver with a simple function call:

uno_solver = unopy.UnoSolver()

Passing options to the Uno solver

Options can be passed to the Uno solver:

uno_solver.set_option("print_solution", True)

Uno mimics the state-of-the-art solvers filterSQP and IPOPT via presets:

uno_solver.set_preset("filtersqp")
# or
uno_solver.set_preset("ipopt")

Solving the model

The model can then be solved by Uno:

result = uno_solver.optimize(model)

Inspecting the result

To inspect the result of the optimization, read the attributes of the result object:

• the optimization status (UNO_SUCCESS, UNO_ITERATION_LIMIT, UNO_TIME_LIMIT, UNO_EVALUATION_ERROR, UNO_ALGORITHMIC_ERROR): result.optimization_status
• the solution status (UNO_NOT_OPTIMAL, UNO_FEASIBLE_KKT_POINT, UNO_FEASIBLE_FJ_POINT, UNO_INFEASIBLE_STATIONARY_POINT, UNO_FEASIBLE_SMALL_STEP, UNO_INFEASIBLE_SMALL_STEP, UNO_UNBOUNDED): result.solution_status
• the objective value of the solution: result.solution_objective
• the primal solution: result.primal_solution
• the dual solution associated with the general constraints: result.constraint_dual_solution
• the dual solution associated with the lower bounds: result.lower_bound_dual_solution
• the dual solution associated with the upper bounds: result.upper_bound_dual_solution
• the primal feasibility residual at the solution: result.solution_primal_feasibility
• the stationarity residual at the solution: result.solution_stationarity
• the complementarity residual at the solution: result.solution_complementarity
• the number of (outer) iterations: result.number_iterations
• the CPU time (in seconds): result.cpu_time
• the number of objective evaluations: result.number_objective_evaluations
• the number of constraint evaluations: result.number_constraint_evaluations
• the number of objective gradient evaluations: result.number_objective_gradient_evaluations
• the number of Jacobian evaluations: result.number_jacobian_evaluations
• the number of Hessian evaluations: result.number_hessian_evaluations
• the number of subproblems solved: result.number_subproblems_solved

How to cite Uno

We have submitted our paper to the Mathematical Programming Computation journal. The preprint is available on ResearchGate.

Until it is published, you can use the following bibtex entry:

@unpublished{VanaretLeyffer2024,
  author = {Vanaret, Charlie and Leyffer, Sven},
  title = {Implementing a unified solver for nonlinearly constrained optimization},
  year = {2024},
  note = {Submitted to Mathematical Programming Computation}
}