The Combinatorial Generation of Objective Targets and Constraints for Large-scale Testing of Optimization Routines

Our primary motivation is the large-scale testing and performance analysis of constrained optimization algorithms. To that end, we wish to randomly generate pairs (f, Ω) consisting of a continuous objective target f and a convex feasibility region Ω contained in its domain. Our challenge is to produce (f, Ω) in such a way that the true solution of the associated constrained optimization problem can be established combinatorially without recourse to an optimization algorithm.