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.. index:: single: linear_programming_protocol .. _linear_programming_protocol/0:
.. rst-class:: right
protocol
linear_programming_protocol
Protocol for immutable linear-program construction, solving, and result inspection.
| Availability:
| logtalk_load(linear_programming(loader))
| Author: Paulo Moura | Version: 1:0:0 | Date: 2026-09-03
| Compilation flags:
| static
| Dependencies: | (none)
| Remarks: | (none)
| Inherited public predicates: | (none)
.. contents:: :local: :backlinks: top
Public predicates
.. index:: new_problem/1 .. _linear_programming_protocol/0::new_problem/1:
new_problem/1 ^^^^^^^^^^^^^^^^^
Creates an empty linear-program problem.
| Compilation flags:
| static
| Template:
| new_problem(Problem)
| Mode and number of proofs:
| new_problem(-compound) - one
.. index:: variable/4 .. _linear_programming_protocol/0::variable/4:
variable/4 ^^^^^^^^^^^^^^
Adds a variable with default bounds. Continuous and integer variables default to zero and positive infinity; binary variables default to zero and one. The variable type is continuous, integer, or binary.
| Compilation flags:
| static
| Template:
| variable(Name,Type,Problem0,Problem)
| Mode and number of proofs:
| variable(+term,+atom,+compound,-compound) - one_or_error
| Exceptions:
| An argument is insufficiently instantiated:
| instantiation_error
| Problem0 is not a linear-program problem:
| type_error(linear_program,Problem0)
| Type is not a supported variable type:
| domain_error(linear_programming_variable_type,Type)
| Name is already declared:
| domain_error(linear_programming_variable,Name)
.. index:: variable/6 .. _linear_programming_protocol/0::variable/6:
variable/6 ^^^^^^^^^^^^^^
Adds a variable with explicit lower and upper bounds. A bound is a number, inf, or -inf as appropriate.
| Compilation flags:
| static
| Template:
| variable(Name,Type,Lower,Upper,Problem0,Problem)
| Mode and number of proofs:
| variable(+term,+atom,+term,+term,+compound,-compound) - one_or_error
| Exceptions:
| An argument is insufficiently instantiated:
| instantiation_error
| Problem0 is not a linear-program problem:
| type_error(linear_program,Problem0)
| Type is not a supported variable type:
| domain_error(linear_programming_variable_type,Type)
| Name is already declared:
| domain_error(linear_programming_variable,Name)
| The bounds are invalid or inconsistent:
| domain_error(linear_programming_bounds,Lower-Upper)
.. index:: constraint/5 .. _linear_programming_protocol/0::constraint/5:
constraint/5 ^^^^^^^^^^^^^^^^
Adds a linear constraint. Coefficients is a list of Coefficient*Variable terms and Sense is =<, >=, or =.
| Compilation flags:
| static
| Template:
| constraint(Coefficients,Sense,RightHandSide,Problem0,Problem)
| Mode and number of proofs:
| constraint(+list(compound),+atom,+number,+compound,-compound) - one_or_error
| Exceptions:
| An argument is insufficiently instantiated:
| instantiation_error
| Problem0 is not a linear-program problem:
| type_error(linear_program,Problem0)
| Coefficients is not a list of coefficient-variable terms:
| type_error(linear_expression,Coefficients)
| Sense is not a supported constraint sense:
| domain_error(linear_programming_constraint_sense,Sense)
| A coefficient references an undeclared variable:
| domain_error(linear_programming_variable,Variable)
.. index:: constraints/3 .. _linear_programming_protocol/0::constraints/3:
constraints/3 ^^^^^^^^^^^^^^^^^
Adds a list of constraint(Coefficients, Sense, RightHandSide) terms.
| Compilation flags:
| static
| Template:
| constraints(Constraints,Problem0,Problem)
| Mode and number of proofs:
| constraints(+list(compound),+compound,-compound) - one_or_error
| Exceptions:
| An argument is insufficiently instantiated:
| instantiation_error
| Constraints is not a list of valid constraint terms:
| type_error(linear_programming_constraints,Constraints)
| Problem0 is not a linear-program problem:
| type_error(linear_program,Problem0)
.. index:: objective/4 .. _linear_programming_protocol/0::objective/4:
objective/4 ^^^^^^^^^^^^^^^
Sets the linear objective. Coefficients is a list of Coefficient*Variable terms and Sense is minimize or maximize.
| Compilation flags:
| static
| Template:
| objective(Coefficients,Sense,Problem0,Problem)
| Mode and number of proofs:
| objective(+list(compound),+atom,+compound,-compound) - one_or_error
| Exceptions:
| An argument is insufficiently instantiated:
| instantiation_error
| Problem0 is not a linear-program problem:
| type_error(linear_program,Problem0)
| Coefficients is not a list of coefficient-variable terms:
| type_error(linear_expression,Coefficients)
| Sense is not a supported objective sense:
| domain_error(linear_programming_objective_sense,Sense)
| The problem already has an objective:
| domain_error(linear_programming_objective,Problem0)
| A coefficient references an undeclared variable:
| domain_error(linear_programming_variable,Variable)
.. index:: problem_from_matrices/8 .. _linear_programming_protocol/0::problem_from_matrices/8:
problem_from_matrices/8 ^^^^^^^^^^^^^^^^^^^^^^^^^^^
Creates a problem from a dense objective vector, objective sense, equality rows and right-hand sides, less-than-or-equal rows and right-hand sides, and variable bounds. Variables are named by their one-based column indices.
| Compilation flags:
| static
| Template:
| problem_from_matrices(Objective,ObjectiveSense,EqualityMatrix,EqualityRightHandSide,InequalityMatrix,InequalityRightHandSide,Bounds,Problem)
| Mode and number of proofs:
| problem_from_matrices(+list(number),+atom,+list(list(number)),+list(number),+list(list(number)),+list(number),+list(pair),-compound) - one_or_error
| Exceptions:
| An argument is insufficiently instantiated:
| instantiation_error
| The matrix and vector dimensions are inconsistent:
| domain_error(linear_programming_dimensions,Objective)
| An input is not a numeric vector, numeric matrix, or valid bounds list:
| type_error(linear_programming_matrix_problem,Objective)
.. index:: solve/2 .. _linear_programming_protocol/0::solve/2:
solve/2 ^^^^^^^^^^^
Solves a linear-program problem using default options and returns a result term. Solver statuses include optimal, infeasible, unbounded, iteration_limit, node_limit, and numerical_error as applicable to the backend.
| Compilation flags:
| static
| Template:
| solve(Problem,Result)
| Mode and number of proofs:
| solve(+compound,-compound) - one_or_error
| Exceptions:
| Problem is a variable:
| instantiation_error
| Problem is not a linear-program problem:
| type_error(linear_program,Problem)
| Problem has no variables:
| domain_error(linear_programming_problem,empty)
| Problem has no objective:
| domain_error(linear_programming_problem,missing_objective)
| Problem contains a variable type unsupported by the backend:
| domain_error(simplex_variable_type,Variable-Type)
| A discrete variable does not have finite bounds:
| domain_error(milp_finite_integer_bounds,Variable-(Lower-Upper))
| A discrete variable domain contains no integer:
| domain_error(milp_integer_domain,Variable-(Lower-Upper))
.. index:: solve/3 .. _linear_programming_protocol/0::solve/3:
solve/3 ^^^^^^^^^^^
Solves a linear-program problem using the specified options and returns a result term. Solver statuses include optimal, infeasible, unbounded, iteration_limit, node_limit, and numerical_error as applicable to the backend.
| Compilation flags:
| static
| Template:
| solve(Problem,Result,Options)
| Mode and number of proofs:
| solve(+compound,-compound,+list(compound)) - one_or_error
| Exceptions:
| Problem is a variable:
| instantiation_error
| Problem is not a linear-program problem:
| type_error(linear_program,Problem)
| Problem has no variables:
| domain_error(linear_programming_problem,empty)
| Problem has no objective:
| domain_error(linear_programming_problem,missing_objective)
| Problem contains a variable type unsupported by the backend:
| domain_error(simplex_variable_type,Variable-Type)
| A discrete variable does not have finite bounds:
| domain_error(milp_finite_integer_bounds,Variable-(Lower-Upper))
| A discrete variable domain contains no integer:
| domain_error(milp_integer_domain,Variable-(Lower-Upper))
| Options is a variable:
| instantiation_error
| Options is neither a variable nor a list:
| type_error(list,Options)
| An element Option of the list Options is a variable:
| instantiation_error
| An element Option of the list Options is neither a variable nor a compound term:
| type_error(compound,Option)
| An element Option of the list Options is a compound term but not a valid option:
| domain_error(option,Option)
.. index:: status/2 .. _linear_programming_protocol/0::status/2:
status/2 ^^^^^^^^^^^^
Returns the result status.
| Compilation flags:
| static
| Template:
| status(Result,Status)
| Mode and number of proofs:
| status(+compound,-atom) - one_or_error
| Exceptions:
| Result is a variable:
| instantiation_error
| Result is not a linear-programming result:
| type_error(linear_programming_result,Result)
.. index:: objective_value/2 .. _linear_programming_protocol/0::objective_value/2:
objective_value/2 ^^^^^^^^^^^^^^^^^^^^^
Returns the optimal objective value. Fails when the result status is not optimal.
| Compilation flags:
| static
| Template:
| objective_value(Result,Value)
| Mode and number of proofs:
| objective_value(+compound,-number) - zero_or_one_or_error
| Exceptions:
| Result is a variable:
| instantiation_error
| Result is not a linear-programming result:
| type_error(linear_programming_result,Result)
.. index:: variable_value/3 .. _linear_programming_protocol/0::variable_value/3:
variable_value/3 ^^^^^^^^^^^^^^^^^^^^
Returns an optimal variable value. Fails when the result status is not optimal or the variable is absent.
| Compilation flags:
| static
| Template:
| variable_value(Result,Variable,Value)
| Mode and number of proofs:
| variable_value(+compound,+term,-number) - zero_or_one_or_error
| Exceptions:
| Result is a variable:
| instantiation_error
| Result is not a linear-programming result:
| type_error(linear_programming_result,Result)
.. index:: statistics/2 .. _linear_programming_protocol/0::statistics/2:
statistics/2 ^^^^^^^^^^^^^^^^
Returns solver statistics stored in a result.
| Compilation flags:
| static
| Template:
| statistics(Result,Statistics)
| Mode and number of proofs:
| statistics(+compound,-list(compound)) - one_or_error
| Exceptions:
| Result is a variable:
| instantiation_error
| Result is not a linear-programming result:
| type_error(linear_programming_result,Result)
.. index:: print_problem/1 .. _linear_programming_protocol/0::print_problem/1:
print_problem/1 ^^^^^^^^^^^^^^^^^^^
Prints a linear-program problem to the current output stream.
| Compilation flags:
| static
| Template:
| print_problem(Problem)
| Mode and number of proofs:
| print_problem(+compound) - one_or_error
| Exceptions:
| Problem is a variable:
| instantiation_error
| Problem is not a linear-program problem:
| type_error(linear_program,Problem)
.. index:: print_solution/1 .. _linear_programming_protocol/0::print_solution/1:
print_solution/1 ^^^^^^^^^^^^^^^^^^^^
Prints a linear-program result to the current output stream.
| Compilation flags:
| static
| Template:
| print_solution(Result)
| Mode and number of proofs:
| print_solution(+compound) - one_or_error
| Exceptions:
| Result is a variable:
| instantiation_error
| Result is not a linear-programming result:
| type_error(linear_programming_result,Result)
Protected predicates
(none)
Private predicates
(none)
Operators
(none)