Inverse lithography which generates model-based patterns theoretically has superior patterning fidelity comparing to conventional rule-based technique. Cost functions are the determinant of performance inverse lithography that is also an optimization problem. However, the design and know-how of cost functions have rarely been discussed. In this paper, we investigate the impacts of various cost functions and their superposition for inverse lithography patterning exploiting a steepest descent algorithm. We research the most generally used objective functions, which are the resist and aerial images, and also deliver a derivation for the aerial image contrast. We then discuss the pattern fidelity and final mask characteristics for simple layouts with a single isolated contact and two nested contacts. Moreover, the convergences which are expressed by edge-placement error (EPE) and contrast versus iteration numbers rapidly attain to steady sate in most hybrid cost functions. All in all, we conclude that a cost function composed of a dominant resist-image component and a minor aerial-image or image-contrast component can carry out a good mask correction and contour targets when using inverse lithography patterning.