Refined necessary conditions in multiobjective optimization with applications to microeconomic modeling

This paper concerns new developments on first-order necessary conditions in set-valued optimization with applications of the results obtained to deriving refined versions of the so-called second fundamental theorem of welfare economics. It is shown that equilibrium marginal prices at local Pareto-type optimal allocations of nonconvex economies are in fact adjoint elements/ multipliers in necessary conditions for fully localized minimizers of appropriate constrained set-valued optimization problems. The latter notions are new in multiobjective optimization and reduce to conventional notions of minima for scalar problems. Our approach is based on advanced tools of variational analysis and generalized differentiation.

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