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DictModel definition

There are 2 ways to define a DictModel. The direct method is:

model = DictModel()

To pass an objective function while constructing the model, use:

model = DictModel(obj)

where obj is a function that takes a single OrderedDict argument.

JuMP model to Nonconvex DictModel

JuMP.jl has an excellent API for defining variables and linear constraints. Using JuMP makes it straightforward to copy a set of linear constraints and variable definitions from a paper. In Nonconvex, you can start with a JuMP model, define variables and constraints using JuMP's API then convert it to a DictModel. For example:

jump_model = JuMP.Model()
@variable jump_model 0 <= x[i=1:3] <= 1
@constraint jump_model sum(x) <= 1
model = DictModel(jump_model)

The objective can also be defined either using JuMP or Nonconvex. Once you convert the JuMP model to a Nonconvex model, you can go ahead and define more variables and constraints and/or set the objective in Nonconvex.

Variable definition

Add a single variable

Each variable in a DictModel has a name which can be a symbol or string. Each named variable can have an arbitrary type, e.g:

  1. Vectors or arrays in general
  2. Dictionaries
  3. Structs
  4. Tuples
  5. NamedTuples
  6. Nested data structures

Vectorization and de-vectorization are handled automatically by Nonconvex.

To add a new named variable to a DictModel with a name :a and lower and upper bounds lb and ub respectively, use:

addvar!(model, :a, lb, ub)

Similar to Model, optional keyword arguments init and integer can be set, and the types of the initial value, lb and ub must be the same.

Add multiple variables

There is no way to add multiple variables simultaneously to a DictModel however a single named variable that's a vector can be added.

Objective definition

To specify an objective function after creating the model, use:

set_objective!(model, obj)

where obj is a function that takes a single OrderedDict argument. The OrderedDict input to obj will be of the same structure, shape and types as the OrderedDict initial solution, lower bounds and upper bounds.

Inequality constraint definition

To define an inequality constraint f(x) <= 0, where f is a Julia function that accepts a single OrderedDict input, use:

add_ineq_constraint!(model, f)

The OrderedDict input to f will be of the same structure, shape and types as the OrderedDict initial solution, lower bounds and upper bounds. The function f can return:

  1. A number, in which case the constraint will be f(x) <= 0
  2. A vector or array of numbers, in which case the constraint will be applied element-wise f(x) .<= 0.
  3. An arbitrary container or data structure, in which case the output will be vectorized first and the constraint will be applied element-wise on the vectorized output.

Equality constraint definition

To define an inequality constraint f(x) == 0, where f is a Julia function that accepts a single OrderedDict input, use:

add_eq_constraint!(model, f)

The OrderedDict input to f will be of the same structure, shape and types as the OrderedDict initial solution, lower bounds and upper bounds. The function f can return:

  1. A number, in which case the constraint will be f(x) == 0
  2. A vector or array of numbers, in which case the constraint will be applied element-wise f(x) .== 0.
  3. An arbitrary container or data structure, in which case the output will be vectorized first and the constraint will be applied element-wise on the vectorized output.