This paper presents an algorithm for constrained black-box and grey-box optimization. It is based on surrogate models developed using input-output data in a trust-region framework. Unlike many current methods, the proposed approach does not require feasible initial point and can handle hard constraints via a novel optimization-based constrained sampling scheme. A two-phase strategy is employed, where the first phase involves finding feasible point through minimizing a smooth constraint violation function (feasibility phase). The second phase improves the objective in the feasible region using the solution of the feasibility phase as starting point (optimization phase). The method is applied to solve 92 test problems and the performance is compared with established derivative-free solvers. The two-phase algorithm outperforms these solvers in terms of number of problems solved and number of samples used. We also apply the algorithm to solve a chemical process design problem involving highly-coupled, nonlinear algebraic and partial differential equations. Published by Elsevier Ltd.