Add solve, solve!, init

lib/OptimizationBase/src/solve.jl

@@ -29,6 +29,147 @@ function Base.showerror(io::IO, e::OptimizerMissingError)
     print(e.alg)
 end
 
+"""
+```julia
+solve(prob::OptimizationProblem, alg::AbstractOptimizationAlgorithm,
+    args...; kwargs...)::OptimizationSolution
+```
+
+For information about the returned solution object, refer to the documentation for [`OptimizationSolution`](@ref)
+
+## Keyword Arguments
+
+The arguments to `solve` are common across all of the optimizers.
+These common arguments are:
+
+  - `maxiters`: the maximum number of iterations
+  - `maxtime`: the maximum amount of time (typically in seconds) the optimization runs for
+  - `abstol`: absolute tolerance in changes of the objective value
+  - `reltol`: relative tolerance  in changes of the objective value
+  - `callback`: a callback function
+
+Some optimizer algorithms have special keyword arguments documented in the
+solver portion of the documentation and their respective documentation.
+These arguments can be passed as `kwargs...` to `solve`. Similarly, the special
+keyword arguments for the `local_method` of a global optimizer are passed as a
+`NamedTuple` to `local_options`.
+
+Over time, we hope to cover more of these keyword arguments under the common interface.
+
+A warning will be shown if a common argument is not implemented for an optimizer.
+
+## Callback Functions
+
+The callback function `callback` is a function that is called after every optimizer
+step. Its signature is:
+
+```julia
+callback = (state, loss_val) -> false
+```
+
+where `state` is an `OptimizationState` and stores information for the current
+iteration of the solver and `loss_val` is loss/objective value. For more
+information about the fields of the `state` look at the `OptimizationState`
+documentation. The callback should return a Boolean value, and the default
+should be `false`, so the optimization stops if it returns `true`.
+
+### Callback Example
+
+Here we show an example of a callback function that plots the prediction at the current value of the optimization variables.
+For a visualization callback, we would need the prediction at the current parameters i.e. the solution of the `ODEProblem` `prob`.
+So we call the `predict` function within the callback again.
+
+```julia
+function predict(u)
+    Array(solve(prob, Tsit5(), p = u))
+end
+
+function loss(u, p)
+    pred = predict(u)
+    sum(abs2, batch .- pred)
+end
+
+callback = function (state, l; doplot = false) #callback function to observe training
+    display(l)
+    # plot current prediction against data
+    if doplot
+        pred = predict(state.u)
+        pl = scatter(t, ode_data[1, :], label = "data")
+        scatter!(pl, t, pred[1, :], label = "prediction")
+        display(plot(pl))
+    end
+    return false
+end
+```
+
+If the chosen method is a global optimizer that employs a local optimization
+method, a similar set of common local optimizer arguments exists. Look at `MLSL` or `AUGLAG`
+from NLopt for an example. The common local optimizer arguments are:
+
+  - `local_method`: optimizer used for local optimization in global method
+  - `local_maxiters`: the maximum number of iterations
+  - `local_maxtime`: the maximum amount of time (in seconds) the optimization runs for
+  - `local_abstol`: absolute tolerance in changes of the objective value
+  - `local_reltol`: relative tolerance  in changes of the objective value
+  - `local_options`: `NamedTuple` of keyword arguments for local optimizer
+"""
+function solve(prob::OptimizationProblem, alg, args...;
+        kwargs...)::AbstractOptimizationSolution
+    if supports_opt_cache_interface(alg)
+        solve!(init(prob, alg, args...; kwargs...))
+    else
+        if prob.u0 !== nothing && !isconcretetype(eltype(prob.u0))
+            throw(NonConcreteEltypeError(eltype(prob.u0)))
+        end
+        _check_opt_alg(prob, alg; kwargs...)
+        __solve(prob, alg, args...; kwargs...)
+    end
+end
+
+"""
+```julia
+init(prob::OptimizationProblem, alg::AbstractOptimizationAlgorithm, args...; kwargs...)
+```
+
+## Keyword Arguments
+
+The arguments to `init` are the same as to `solve` and common across all of the optimizers.
+These common arguments are:
+
+  - `maxiters` (the maximum number of iterations)
+  - `maxtime` (the maximum of time the optimization runs for)
+  - `abstol` (absolute tolerance in changes of the objective value)
+  - `reltol` (relative tolerance  in changes of the objective value)
+  - `callback` (a callback function)
+
+Some optimizer algorithms have special keyword arguments documented in the
+solver portion of the documentation and their respective documentation.
+These arguments can be passed as `kwargs...` to `init`.
+
+See also [`solve(prob::OptimizationProblem, alg, args...; kwargs...)`](@ref)
+"""
+function init(prob::OptimizationProblem, alg, args...; kwargs...)::AbstractOptimizationCache
+    if prob.u0 !== nothing && !isconcretetype(eltype(prob.u0))
+        throw(NonConcreteEltypeError(eltype(prob.u0)))
+    end
+    _check_opt_alg(prob::OptimizationProblem, alg; kwargs...)
+    cache = __init(prob, alg, args...; prob.kwargs..., kwargs...)
+    return cache
+end
+
+"""
+```julia
+solve!(cache::AbstractOptimizationCache)
+```
+
+Solves the given optimization cache.
+
+See also [`init(prob::OptimizationProblem, alg, args...; kwargs...)`](@ref)
+"""
+function solve!(cache::AbstractOptimizationCache)::AbstractOptimizationSolution
+    __solve(cache)
+end
+
 # Algorithm compatibility checking function
 function _check_opt_alg(prob::SciMLBase.OptimizationProblem, alg; kwargs...)
     !SciMLBase.allowsbounds(alg) && (!isnothing(prob.lb) || !isnothing(prob.ub)) &&