Add error message when NLopt AUGLAG algorithms are used without local_method

Fixes #1020

NLopt's AUGLAG algorithms require a local optimization method to be specified.
Previously, using them without a local_method would result in undefined behavior
(returning wrong results like [0.0, 0.0] with Inf objective).

This commit adds a clear error message when AUGLAG algorithms are used without
specifying a local_method parameter, helping users understand the correct usage.

Changes:
- Add check in __map_optimizer_args! to detect AUGLAG algorithms without local_method
- Provide helpful error message with usage example
- Add test cases to verify the error is thrown correctly

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <[email protected]>

Author: ChrisRackauckas

lib/OptimizationNLopt/src/OptimizationNLopt.jl

@@ -68,6 +68,15 @@ function __map_optimizer_args!(cache::OptimizationCache, opt::NLopt.Opt;
         local_maxtime::Union{Number, Nothing} = nothing,
         local_options::Union{NamedTuple, Nothing} = nothing,
         kwargs...)
+
+    # Check if AUGLAG algorithm requires local_method
+    alg_str = string(opt.algorithm)
+    if occursin("AUGLAG", alg_str) && local_method === nothing
+        error("NLopt.$(opt.algorithm) requires a local optimization method. " *
+              "Please specify a local_method, e.g., solve(prob, NLopt.$(opt.algorithm)(); " *
+              "local_method = NLopt.LN_NELDERMEAD())")
+    end
+
     if local_method !== nothing
         if isa(local_method, NLopt.Opt)
             if ndims(local_method) != length(cache.u0)

lib/OptimizationNLopt/test/runtests.jl

@@ -149,6 +149,10 @@ using Test, Random
         # @test sol.retcode == ReturnCode.Success
         @test 10 * sol.objective < l1
 
+        # Test that AUGLAG without local_method throws an error
+        @test_throws ErrorException solve(prob, NLopt.LN_AUGLAG())
+        @test_throws ErrorException solve(prob, NLopt.LD_AUGLAG())
+
         function con2_c(res, x, p)
             res .= [x[1]^2 + x[2]^2 - 1.0, x[2] * sin(x[1]) - x[1] - 2.0]
         end