Sage Reference Manual: Numerical Optimization - Mirrors

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Sage Reference Manual: Numerical Optimization, Release 6.1.1 True if the variable is real; False otherwise. EXAMPLE: sage: p = MixedIntegerLinearProgram() sage: v = p.new_variable() sage: p.set_objective(v[1]) sage: p.is_real(v[1]) True sage: p.set_binary(v[1]) sage: p.is_real(v[1]) False sage: p.set_real(v[1]) sage: p.is_real(v[1]) True linear_constraints_parent() Return the parent for all linear constraints See linear_functions for more details. EXAMPLES: sage: p = MixedIntegerLinearProgram() sage: p.linear_constraints_parent() Linear constraints over Real Double Field linear_function(x) Construct a new linear function EXAMPLES: sage: p = MixedIntegerLinearProgram() sage: p.linear_function({1:3, 4:5}) 3*x_1 + 5*x_4 This is equivalent to: sage: p({1:3, 4:5}) 3*x_1 + 5*x_4 linear_functions_parent() Return the parent for all linear functions EXAMPLES: sage: p = MixedIntegerLinearProgram() sage: p.linear_functions_parent() Linear functions over Real Double Field new_variable(real=False, binary=False, integer=False, dim=1, name=’‘) Returns an instance of MIPVariable associated to the current instance of MixedIntegerLinearProgram. A new variable x is defined by: sage: p = MixedIntegerLinearProgram() sage: x = p.new_variable() It behaves exactly as a usual dictionary would. It can use any key argument you may like, as x[5] or x["b"], and has methods items() and keys(). Any of its fields exists, and is uniquely defined. 20 Chapter 2. Mixed integer linear programming
Sage Reference Manual: Numerical Optimization, Release 6.1.1 By default, all x[i] are assumed to be non-negative reals. They can be defined as binary through the parameter binary=True (or integer with integer=True). Lower and upper bounds can be defined or re-defined (for instance when you want some variables to be negative) using MixedIntegerLinearProgram methods set_min and set_max. INPUT: •dim (integer) – Defines the dimension of the dictionary. If x has dimension 2, its fields will be of the form x[key1][key2]. •binary, integer, real (boolean) – Set one of these arguments to True to ensure that the variable gets the corresponding type. The default type is real. •name (string) – Associates a name to the variable. This is only useful when exporting the linear program to a file using write_mps or write_lp, and has no other effect. EXAMPLE: sage: p = MixedIntegerLinearProgram() To define two dictionaries of variables, the first being of real type, and the second of integer type :: sage: x = p.new_variable(real=True) sage: y = p.new_variable(dim=2, integer=True) sage: p.add_constraint(x[2] + y[3][5], max=2) sage: p.is_integer(x[2]) False sage: p.is_integer(y[3][5]) True An exception is raised when two types are supplied sage: z = p.new_variable(real = True, integer = True) Traceback (most recent call last): ... ValueError: Exactly one of the available types has to be True number_of_constraints() Returns the number of constraints assigned so far. EXAMPLE: sage: p = MixedIntegerLinearProgram() sage: p.add_constraint(p[0] - p[2], min = 1, max = 4) sage: p.add_constraint(p[0] - 2*p[1], min = 1) sage: p.number_of_constraints() 2 number_of_variables() Returns the number of variables used so far. Note that this is backend-dependent, i.e. we count solver’s variables rather than user’s variables. An example of the latter can be seen below: Gurobi converts double inequalities, i.e. inequalities like m
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CHAPTER SIX INDICES AND TABLES •
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BIBLIOGRAPHY [HPS08] J. Hoffstein,
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PYTHON MODULE INDEX n sage.numerica
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INDEX A add_col() (sage.numerical.b
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