Refined necessary conditions in multiobjective optimization with applications to microeconomic modeling
Truong Q. Bao, Boris S. Mordukhovich · Discrete and Continuous Dynamical Systems · 2011
This paper concerns new developments onfirst-order necessary conditions in set-valued optimization withapplications of the results obtained to deriving refined versionsof the so-called second fundamental theorem of welfare economics.It is shown that equilibrium marginal prices at local Pareto-typeoptimal allocations of nonconvex economies are in fact adjointelements/ multipliers in necessary conditions for fully localizedminimizers of appropriate constrained set-valued optimizationproblems. The latter notions are new in multiobjectiveoptimization and reduce to conventional notions of minima forscalar problems. Our approach is based on advanced tools ofvariational analysis and generalized differentiation.