In this paper, we present constraint-partitioned sim- ulated annealing (CPSA), an algorithm that extends our previous constrained simulated annealing (CSA) for constrained optimization. The algorithm is based on the theory of extended saddle points (ESPs). By decomposing the ESP condition into multiple neces- sary conditions, CPSA partitions a problem by its constraints into subproblems, solves each indepen- dently using CSA, and resolves those violated global constraints across the subproblems. Because each subproblem is exponentially simpler and the number of global constraints is very small, the complexity of solving the original problem is significantly reduced. We state without proof the asymptotic convergence of CPSA with probability one to a constrained global minimum in discrete space. Last, we evaluate CPSA on some continuous constrained benchmarks.