Adaptive Power Allocation (PA) algorithms with different criteria for a cooperative Multiple-Input Multiple-Output (MIMO) network equipped with Distributed Space-Time Coding (DSTC) are proposed and evaluated. Joint constrained optimization algorithms to determine the power allocation parameters, the channel parameters and the receive filter are proposed for each transmitted stream in each link. Linear receive filter and maximum-likelihood (ML) detection are considered with Amplify-and-Forward (AF) and Decode-and-Forward (DF) cooperation strategies. In the proposed algorithms, the elements in the PA matrices are optimized at the destination node and then transmitted back to the relay nodes via a feedback channel. The effects of the feedback errors are considered. Linear MMSE expressions and the PA matrices depend on each other and are updated iteratively. Stochastic gradient (SG) algorithms are developed with reduced computational complexity. Simulation results show that the proposed algorithms obtain significant performance gains as compared to existing power allocation schemes.