Parallel radio frequency transmission has recently been explored as a means of tailoring the spatial response of MR excitation. In particular, parallel transmission is increasingly used to accelerate radio frequency pulses that rely on time-varying gradient fields to achieve selectivity in multiple dimensions. The design of the underlying multiple-channel radio frequency waveforms is mostly based on regularized least-squares optimization in close analogy with image reconstruction in parallel imaging. However, this analogy has important limitations. Unlike image reconstruction, the design of radio frequency waveforms is subject to multiple strict constraints, which arise from technical power limits, as well as safety limits on local and global energy deposition in vivo. To optimize excitation profiles under such strict constraints, it is proposed to depart from the regularization strategy and rely on semidefinite programming instead. To render this approach fast, it is performed in a reduced search space, which is obtained by initial Lanczos iteration. The proposed algorithm is demonstrated to enable efficient pulse optimization within exactly the given constraints, including local specific absorption rate limits for multiple compartments. It is also shown that the proposed approach readily accommodates advanced forward models of the excitation process, including the effects of local off-resonance and transverse relaxation.