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We explore novel approaches for solving nonlinear optimization problems withunrelaxable bound constraints, which must be satisfied before the objectivefunction can be evaluated. Our method reformulates the unrelaxablebound-constrained problem as an unconstrained optimization problem that isamenable to existing unconstrained optimization methods. The reformulationrelies on a domain warping to form a merit function; the choice of the warpingdetermines the level of exactness with which the unconstrained problem can beused to find solutions to the bound-constrained problem, as well as keyproperties of the unconstrained formulation such as smoothness. We developtheory when the domain warping is a multioutput sigmoidal warping, and weexplore the practical elements of applying unconstrained optimization methodsto the formulation. We develop an algorithm that exploits the structure of thesigmoidal warping to guarantee that unconstrained optimization algorithmsapplied to the merit function will find a stationary point to the desiredtolerance.

Modeling Approaches for Addressing Simple Unrelaxable Constraints with Unconstrained Optimization Methods