A new constrained space mapping algorithm is presented. This algorithm is based on aggressive space mapping type algorithm. Orthogonal projection is used to handle the constraints. The new method has advantage of simplicity without sacrificing mathematical robustness of space mapping. Proof of the convergence of the proposed method for convex constraints case is presented. Modified Broyden's method is used to improve the method's stability. The proposed algorithm is used to optimize a multilayer low-temperature cofired ceramic bandpass filter. Parameter extraction is done using circuit tuning based on physical augmentation. The results show the proposed algorithm is effective and efficient. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2012.