In this paper the previously published optimization algorithm for thermal dose optimization is tested with numerical simulations. The simulations concern the thermal dose optimization in ultrasound surgery of the breast. The optimization algorithm is extended by setting the inequality constraint approximations to temperature in healthy tissue as well as in tumor region. In addition, the simulations are accomplished in realistic 3D geometry with varying thermal parameters. Another topic of the paper is to show the potential of the hemispherical phased array applicator for ultrasound surgery of the breast. With such an applicator larger tissue volumes can be treated with shorter time as compared to single element transducers. In simulations the geometrical focus of the applicator was placed mechanically in the middle of the treatable region. The whole tumor region was then scanned electrically by changing the phase of the emitted wave from individual elements. The simulations indicate that a feasible treatment plan can be achieved. In simulated cases the desired thermal dose was achieved for tumors with diameter from 1.5 to 2.4 cm, depending on the position of tumor. The maximum temperature limitations of 45 degrees C in healthy region and 80 degrees C in tumor region can be maintained in all simulations.