Ahead of the new asset management era that calls for sustainable investments, the limitations of the traditional bi-objective mean–variance framework need to be resolved, to accommodate responsible investment objectives. In this paper, we propose a multi-objective minimax-based portfolio optimization model, attempting to simultaneously maximize the risk performance of the three typical ESG investment objectives. Also, apart from the systematic risk, the underlying formulation incorporates the controversy dimension, associated with each company participating in the optimal ESG portfolio. The validity of the proposed model is assessed through an extensive empirical testing on the EURO STOXX 50, the DAX, the CAC 40 and the DJIA, for a 5-year period. The results are considered as highly satisfactory, since the optimal ESG portfolios produced by the model provide consistently higher risk-adjusted returns, in comparison to their respective market benchmarks.