This paper considers a $K$-user multiple-input single-output (MISO) interference channels for simultaneous wireless information and power transfer (SWIPT), where each multi-antenna transmitter serves a single-antenna receiver per user pair. All receivers perform simultaneously information processing and energy harvesting (EH) based on the receive power-splitting (PS) architectures. Assuming imperfect channel state information (CSI) at the transmitters, we develop an optimal robust transceiver design scheme that minimizes the total transmission power under the worst-case signal-to-interference-plus-noise ratio (SINR) and energy harvesting (EH) constraints at the receivers, by jointly optimizing transmit beamforming and receive PS ratio per receiver. When the CSI uncertainties are bounded by ellipsoidal regions, it is shown that the worst-case SINR and EH constraints per receiver can be recast into quadratic matrix inequality forms. Leveraging semidefinite relaxation technique, the intended robust beamforming and PS (BFPS) problem can be relaxed as a tractable (centralized) semidefinite program (SDP). More importantly, relying on the state-of-the-art alternating direction method of multipliers (ADMM) in convex optimization, we propose a {\em decentralized} algorithm capable of computing the optimal robust BFPS scheme with local CSI and limited information exchange among the transmitters. It is shown the proposed decentralized algorithm is guaranteed to converge to the optimal centralized solution. Numerical results are provided to demonstrate the merits of the proposed approaches.