Add example and format

Author: AlCap23

docs/src/index.md

@@ -41,21 +41,21 @@ packages.
 
 ## Overview of the Optimizers
 
-| Package                 | Local Gradient-Based | Local Hessian-Based | Local Derivative-Free | Box Constraints | Local Constrained | Global Unconstrained | Global Constrained |
-|:----------------------- |:--------------------:|:-------------------:|:---------------------:|:---------------:|:-----------------:|:--------------------:|:------------------:|
-| BlackBoxOptim           | ❌                    | ❌                   | ❌                   |✅              | ❌                 | ✅                    | ❌                  |✅              
-| CMAEvolutionaryStrategy | ❌                    | ❌                   | ❌                   |✅                | ❌                 | ✅                    | ❌                  |
-| Evolutionary            | ❌                    | ❌                   | ❌                   |✅                | ❌                 | ✅                    | 🟡                  |
-| Flux                    | ✅                    | ❌                   | ❌                   |❌                | ❌                 | ❌                    | ❌                  |
-| GCMAES                  | ❌                    | ❌                   | ❌                   |✅                | ❌                 | ✅                    | ❌                  |
-| MathOptInterface        | ✅                    | ✅                   | ✅                   |✅                | ✅                 | ✅                    | 🟡                  |
-| MultistartOptimization  | ❌                    | ❌                   | ❌                   |✅                | ❌                 | ✅                    | ❌                  |
-| Metaheuristics          | ❌                    | ❌                   | ❌                   |✅                | ❌                 | ✅                    | 🟡                  |
-| NOMAD                   | ❌                    | ❌                   | ❌                   |✅                | ❌                 | ✅                    | 🟡                  |
-| NLopt                   | ✅                    | ❌                   | ✅                   |✅                | 🟡                 | ✅                    | 🟡                  |
-| Nonconvex               | ✅                    | ✅                   | ✅                   |✅                | 🟡                 | ✅                    | 🟡                  |
-| Optim                   | ✅                    | ✅                   | ✅                   |✅                | ✅                 | ✅                    | ✅                  |
-| QuadDIRECT              | ❌                    | ❌                   | ❌                   |✅                | ❌                 | ✅                    | ❌                  |
+| Package                 | Local Gradient-Based | Local Hessian-Based | Local Derivative-Free | Box Constraints | Local Constrained | Global Unconstrained | Global Constrained   |
+|:----------------------- |:--------------------:|:-------------------:|:---------------------:|:---------------:|:-----------------:|:--------------------:|:--------------------:|
+| BlackBoxOptim           | ❌                    | ❌                   | ❌                     | ✅               | ❌                 | ✅                    | ❌                  ✅ |
+| CMAEvolutionaryStrategy | ❌                    | ❌                   | ❌                     | ✅               | ❌                 | ✅                    | ❌                    |
+| Evolutionary            | ❌                    | ❌                   | ❌                     | ✅               | ❌                 | ✅                    | 🟡                    |
+| Flux                    | ✅                    | ❌                   | ❌                     | ❌               | ❌                 | ❌                    | ❌                    |
+| GCMAES                  | ❌                    | ❌                   | ❌                     | ✅               | ❌                 | ✅                    | ❌                    |
+| MathOptInterface        | ✅                    | ✅                   | ✅                     | ✅               | ✅                 | ✅                    | 🟡                    |
+| MultistartOptimization  | ❌                    | ❌                   | ❌                     | ✅               | ❌                 | ✅                    | ❌                    |
+| Metaheuristics          | ❌                    | ❌                   | ❌                     | ✅               | ❌                 | ✅                    | 🟡                    |
+| NOMAD                   | ❌                    | ❌                   | ❌                     | ✅               | ❌                 | ✅                    | 🟡                    |
+| NLopt                   | ✅                    | ❌                   | ✅                     | ✅               | 🟡                 | ✅                    | 🟡                    |
+| Nonconvex               | ✅                    | ✅                   | ✅                     | ✅               | 🟡                 | ✅                    | 🟡                    |
+| Optim                   | ✅                    | ✅                   | ✅                     | ✅               | ✅                 | ✅                    | ✅                    |
+| QuadDIRECT              | ❌                    | ❌                   | ❌                     | ✅               | ❌                 | ✅                    | ❌                    |
 
 ✅ = supported
 

docs/src/optimization_packages/mathoptinterface.md

@@ -76,3 +76,35 @@ opt = OptimizationMOI.MOI.OptimizerWithAttributes(Juniper.Optimizer,
                                                                                                              "print_level" => 0))
 sol = solve(prob, opt)
 ```
+
+#### Using Integer Constraints
+
+The following shows how to use integer linear programming within `Optimization`. We will solve the classical Knapsack Problem using `Juniper.jl`.
+
+  - [`Juniper.Optimizer`](https://github.com/lanl-ansi/Juniper.jl)
+  - Juniper requires a nonlinear optimizer to be set via the `nl_solver` option,
+    which must be a MathOptInterface-based optimizer. See the
+    [Juniper documentation](https://github.com/lanl-ansi/Juniper.jl) for more
+    detail.
+  - Allows only for binary decisions
+
+```@example MOI
+v = [1.0, 2.0, 4.0, 3.0]
+w = [5.0, 4.0, 3.0, 2.0]
+W = 4.0
+u0 = [0.0, 0.0, 0.0, 1.0]
+
+optfun = OptimizationFunction((u, p) -> -v'u, cons = (res, u, p) -> res .= w'u,
+                              Optimization.AutoForwardDiff())
+
+optprob = OptimizationProblem(optfun, u0; lb = zero.(u0), ub = one.(u0),
+                              int = ones(Bool, length(u0)),
+                              lcons = [-Inf;], ucons = [W;])
+
+nl_solver = OptimizationMOI.MOI.OptimizerWithAttributes(Ipopt.Optimizer,
+                                                        "print_level" => 0)
+minlp_solver = OptimizationMOI.MOI.OptimizerWithAttributes(Juniper.Optimizer,
+                                                           "nl_solver" => nl_solver)
+
+res = solve(optprob, minlp_solver)
+```

docs/src/tutorials/intro.md

@@ -45,10 +45,13 @@ sol.original
 ```
 
 ## Defining the objective function
+
 Optimization.jl assumes that your objective function takes two arguments `objective(x, p)`
-1. The optimization variables `x`. 
-2. Other parameters `p`, such as hyper parameters of the cost function. 
-If you have no “other parameters”, you can  safely disregard this argument. If your objective function is defined by someone else, you can create an anonymous function that just discards the extra parameters like this
+
+ 1. The optimization variables `x`.
+ 2. Other parameters `p`, such as hyper parameters of the cost function.
+    If you have no “other parameters”, you can  safely disregard this argument. If your objective function is defined by someone else, you can create an anonymous function that just discards the extra parameters like this
+
 ```julia
 obj = (x, p) -> objective(x) # Pass this function into OptimizationFunction
 ```