This work extends cyclic coordinate descent to efficiently satisfy multiple spatial constraints, respect the secondary structure of proteins., and work with reduced backbone protein models. Reduced models allow us to treat large systems that are intractable under all-atom models. In addition, this thesis combines the satisfaction of multiple spatial constraints with conformational sampling and energy minimization techniques to generate spatially constrained biomolecular structures that are energetically stable under physiological conditions. The experiments in this thesis demonstrate the relevance and robustness of our method on three areas of applications: loop closure; backbone reconstruction, and physical trajectory recovery. Addressing the problem of loop closure, we obtain ensembles of spatially constrained conformations whose energy landscape is in agreement with laboratory experimental results on the energetic stability of the proteins at hand. Our experiments on backbone reconstruction agree with results from statistical approaches to this problem, but in addition guarantee the energetic feasibility of the completed models. (Abstract shortened by UMI.)