Added preliminary benchmarks for eq/ineq problems with free vars

Author: alonsoC1s

benchmarks/OptimizationCUTEst/CUTEst.jmd

@@ -54,6 +54,41 @@ function get_stats(sol, ::OptimizationMOI.MOI.OptimizerWithAttributes)
     return (length(sol.u), MOI.get(sol.original.model, MOI.SolveTimeSec()),
         "Ipopt", Symbol(sol.retcode))
 end
+
+function run_benchmarks(problems, optimizers)
+    problem = String[]
+    n_vars = Int64[]
+    secs = Float64[]
+    solver = String[]
+    retcode = Symbol[]
+
+    optz = length(optimizers)
+    n = length(problems)
+
+    broadcast(c -> sizehint!(c, optz * n), [problem, n_vars, secs, solver, retcode])
+
+    for prob_name in problems
+        nlp_prob = CUTEstModel(prob_name)
+        prob = OptimizationNLPModels.OptimizationProblem(nlp_prob, Optimization.AutoForwardDiff())
+        for optimizer in optimizers
+            sol = solve(prob, optimizer; maxiters = 1e7)
+
+            @info "Solved $(prob_name) with $(optimizer)"
+            vars, time, alg, code = get_stats(sol, optimizer)
+
+            push!(problem, prob_name)
+            push!(n_vars, vars)
+            push!(secs, time)
+            push!(solver, alg)
+            push!(retcode, code)
+
+        end
+        finalize(nlp_prob)
+    end
+
+    return DataFrame(problem = problem, n_vars = n_vars, secs = secs, solver = solver,
+        retcode = retcode)
+end
 ```
 
 ## Unconstrained problems
@@ -63,48 +98,54 @@ terms of the time to solution with respect to the number of variables.
 
 ```julia
 unc_problems = CUTEst.select(contype="unc")
-n = length(unc_problems)
-optz = length(optimizers)
 
-problem = String[]
-n_vars = Int64[]
-secs = Float64[]
-solver = String[]
-retcode = Symbol[]
-
-broadcast(c -> sizehint!(c, optz * n), [problem, n_vars, secs, solver, retcode])
+# Analysis
+unc_results =  run_benchmarks(unc_problems, optimizers)
 
-for prob_name in unc_problems
-    @show prob_name
-    nlp_prob = CUTEstModel(prob_name)
-    prob = OptimizationNLPModels.OptimizationProblem(nlp_prob, Optimization.AutoForwardDiff())
-    for optimizer in optimizers
-        sol = solve(prob, optimizer; maxiters = 1e7)
+@df unc_results scatter(:n_vars, :secs,
+        group = :solver,
+        xlabel = "n. variables",
+        ylabel = "secs.",
+        title = "Time to solution by optimizer and number of vars",
+    )
+```
 
-        @info "Solved $(prob_name) with $(optimizer)"
-        vars, time, alg, code = get_stats(sol, optimizer)
+## Equality/Inequality constrained problems with unbounded variables
 
-        push!(problem, prob_name)
-        push!(n_vars, vars)
-        push!(secs, time)
-        push!(solver, alg)
-        push!(retcode, code)
+These problems have a constraint function that's subject to either equality or inequality
+constraints, but the variables themselves are free. CUTEst contains 285 problems with
+equality constraints and 114 with inequality constraints for a total of 299.
 
-    end
-    finalize(nlp_prob)
+We start by analyzing the equality-constrained problems, of which there are 285. The
+following figure shows the time to solution as a function of number of variables by
+optimizer.
 
-    break
-end
+```julia
+eq_unb_problems = CUTEst.select(min_con=1, only_equ_con=true, only_free_var=true)
 
 # Analysis
-unc_results = DataFrame(problem = problem, n_vars = n_vars, secs = secs, solver = solver,
-    retcode = retcode)
+eq_unb_results =  run_benchmarks(unc_problems, optimizers)
 
-@df unc_results scatter(:nvars, :secs,
+@df eq_unb_results scatter(:n_vars, :secs,
         group = :solver,
         xlabel = "n. variables",
         ylabel = "secs.",
         title = "Time to solution by optimizer and number of vars",
     )
 ```
 
+Next, we examine the same relationship for problems with inequality-constrained problems.
+
+```julia
+neq_unb_problems = CUTEst.select(min_con=1, only_ineq_con=true, only_free_var=true)
+
+# Analysis
+neq_unb_results =  run_benchmarks(unc_problems, optimizers)
+
+@df neq_unb_results scatter(:n_vars, :secs,
+        group = :solver,
+        xlabel = "n. variables",
+        ylabel = "secs.",
+        title = "Time to solution by optimizer and number of vars",
+    )
+```