Initial package implementation

[dnguyen227]

Sample how we'd use this:

using DisjunctiveProgramming, DisjunctiveAlgorithms, Gurobi, Ipopt
import DisjunctiveAlgorithms as DA

model = GDPModel(() -> DA.Optimizer(Ipopt.Optimizer, Gurobi.Optimizer))
set_silent(model)
@variable(model, 0 <= x <= 10)
@variable(model, Y[1:2], Logical)
@constraint(model, x <= 3, Disjunct(Y[1]))
@constraint(model, x^2 == 64, Disjunct(Y[2]))
@disjunction(model, Y)
@objective(model, Max, x)
optimize!(model, gdp_method = Direct())

# status
termination_status(model)   # MOI.LOCALLY_SOLVED
primal_status(model)        # MOI.FEASIBLE_POINT
raw_status(model)           # solver-reported string from the LOA loop
result_count(model)         # 1
is_solved_and_feasible(model)

#obj and bounds
objective_value(model)      # 8.0
objective_bound(model)      # master bound at termination
relative_gap(model)

# solution (can't get duals)
value(x)                    # 8.0
value(Y[1])                 # false
value(Y[2])                 # true
value.(Y)                   # Bool vector

# Solve statistics
solve_time(model)
solver_name(model)          # "DisjunctiveAlgorithms"

# Algorithm attributes read back through JuMP
get_attribute(model, DA.Algorithm())
get_attribute(model, DA.NumIterationLimit())
get_attribute(model, DA.ConvergenceTolerance())

# example of calls not supported.
# dual(con)                 # DualStatus is always NO_SOLUTION
# value(con)                # ConstraintPrimal is refused, not computed

[dnguyen227]

@pulsipher ready for review.

[pulsipher]

A few comments/questions:

• I believe this requires that we first at support for MOI disjunctions in DisjunctiveProgramming, right?
• It doesn't appear that this optimizer supports the full MOI API for queries (i.e., not requiring the user to call the inner solver directly)
• Are the methods in the main src folder truly general and not specific to LOA? (especially master.jl and nlp.jl)
• It would be good to have a test for the natural user interface via DisjunctiveProgramming

[pulsipher]

generally, try catch statements should be avoided