Multi-objective control problem with generalized H-2-norms as criteria, as well as its dual problem with generalized gamma(0)-norms, is studied. By using a scalar multi-objective cost function in the form of Germeyer convolution we derive necessary conditions for Pareto optimality and characterize Pareto optimal controllers in terms of LMIs as optimal solutions for this function. Optimal protection of a high storey building from vibration is then considered in the novel multi-objective framework as an application of the approach proposed. (C) 2018 Elsevier Ltd. All rights reserved.