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In this work, we investigate the performance of a reconfigurable intelligent surface (RIS)-aided multi-user simultaneous wireless information and power transfer (SWIPT) network, where a multiple-input multiple-output (MIMO) base station (BS) serves multiple MIMO information receivers (IRs) while ensuring a minimum harvested power at multiple MIMO energy receivers (ERs). In order to improve the energy efficiency (EE) of the network, we consider a pricing-based performance metric called network utility. We then establish an optimization framework to jointly optimize the transmit precoding matrix (TPM) and phase shift matrix (PSM) to maximize the network utility function with constraints on the available transmit power at BS, minimum harvested power required at each ER, and unit modulus phase shift condition at RIS. Due to the non-convex nature of this problem, we divide it into two sub-problems where a sub …