1. A radio communication apparatus for transmitting a radio signal to multiple users via multiple transmit antenna groups at appropriate transmit power levels, each of the transmit antenna groups including one or more transmit antennas, the transmit antenna groups having respective transmit power constraints, the apparatus comprising: a precoding unit configured to perform precoding on signals modulated for individual users and generate transmit weight related information; an optimum transmit power calculation unit configured to receive the transmit weight related information from the precoding unit and calculate a transmit power level to optimize an objective function in accordance with an interior point method, the objective function resulting from addition of a barrier function adjusted with a barrier parameter to an original objective function associated with a constrained optimization problem; and a transmission unit configured to transmit a radio signal at the calculated transmit power level, wherein the original objective function comprises a function of respective channel capacities for individual users derived from the transmit weight related information, and wherein the optimum transmit power calculation unit is configured to adaptively update a logarithm of the barrier parameter and use a gradient obtained through a high-order differential with the logarithm of the barrier parameter to calculate the transmit power level to optimize the resulting objective function.