Modifications of the methods for finding the global extremum of multi-parametric performance indicators are developed, taking into account the structural features of the quality assessment criteria used in predicting the defining characteristics of composites. The article analyzes promising ways to increase the potential opportunities associated with the improvement of methods for constructing optimal directions for finding the absolute minimum of efficiency indicators associated with solving problems of predicting the residual life, reliability, and durability of polymer composites under the influence of extreme environmental factors and operational loads. The comparative analysis of existing approaches and their possible modifications allowed us to conclude that the most promising opportunities for the effective construction of globally optimal solutions in refined variational formulations of inverse forecasting problems are associated with the development of a methodology for effectively narrowing the search areas containing globally optimal solutions. The results of comparative computational experiments are presented.