Lexicographical problems of linear programming

Lexicographic multi-objective road pricing optimization considering land use and transportation effects

“…Equation ( 8) states that there exists an integer k, such that the value of the k th -most important objective given by  is larger than that given by '  , and for the objectives (objective) that have (has) a higher order than the k th -most important objective, their values (its value) obtained from  and '  are (is) equal (Podinovskii, 1972). In contrast, we say that  and '  are equivalent: Kerrigan and Maciejowski (2002) have proved that a lexicographic optimal solution is a special type of Pareto optimal solution that considers the order of the objectives.…”

Metrics Matter in Community Detection

“…Implementation details The leximin method is implemented in AMPL [33]. While the hierarchical MCFP could be expressed as a single LP, we exploit the lexicographic problem structure to decompose the problem into a sequence of N − 1 smaller, subordinate LPs [34]. Using AMPL's CPLEX backend, the method solves the LP of Dong et al's triples formulation of the MCFP [35].…”

Lexicographic quasiconcave multiobjective programming

“…In Decision Theory, a new criterion, which in a discrete setting reduces to lexicographic decision, was suggested in Behringer [ 1975]. Other papers containing the notion of lexicographic optimization are Brucker [ 1972], Dinkelbach [ 1971 ]; Isermann [1974 ], Kelleher [1970], Menges und Diehl [1966], Podinovskii [1972]. For a more detailed discussion of these see Behringer [(b)].…”