Origins of Soviet multi-objective programming; a framework for approaching Soviet multi-objective programming. Part 1 No articulation of preferences: Salukvadze's ideal distance minimization method; multi-objective programming and the maximal effectiveness principle; Velichenko's minimax method. Part 2 A priori articulation of preferences: multi-objective decomposition for scalar problems. Part 3 Progressive articulation of preferences: the hierarchical decomposition approach to high dimension multi-objective programming problems; the STEM method; multi-objective graph theory; method of constraints; parameter space investigation method; the random search method; the vector-relaxation method; the interactive grid method; adaptive search method for multi-objective optimization; pareto boundary maps. Part 4 Posteriori articulation of preferences: dynamic and stochastic multi-objective programming; the reachable sets method; piecewise linear approximation. Part 5 Other noteworthy research in multi-objective programming: methodological research at VNIISI; Rastrigin and Eiduk's methodological work; the theory of parametric scalarization; miscellaneous other research; some concluding observations. Appendices: method of constraints - theoretical considerations; illustrative example - linear programming problem; method of sequential analysis; illustrative example - integer programming problem without side constraints; computational experience; terminology; Soviet books on multi-objective subjects; Soviet researchers' institutional affiliations; cyrillic-Roman transliteration conventions; Soviet sources, non-Soviet sources.