Lagrange multiplers for pareto nonsmooth programming problems in banach spaces

Extensions of Fréchet ϵ-Subdifferential Calculus and Applications

“…Then a necessary condition for x to be an · -solution of is that there exist λ ∈ 0 ∞ and y * ∈ S * z * ∈ Z * not both zero such that 0 ∈ λ∂ f x +∂ y * • G x +∂ z * • H x y * G x = 0 For exact optimal solutions ( = 0), a similar result was obtained in [24,26] for the case where Y is a finite-dimensional space (say, Y = n and S = n + , and in [1,6] for Ioffe's approximate subdifferential. Note that in general, the limiting Fréchet subdifferential is smaller than the approximate subdifferential.…”

Tangent and Normal Cones in Nonconvex Multiobjective Optimization

“…The corresponding results in Banach spaces for weak and/or Pareto optimality are given in [6], [16] and [19]. A more general formulation is given in [7]. Some special cases with proper Pareto optimality are considered in [4].…”

Duality in Vector Optimization Under Type 1 α-Invexity in Banach Spaces

“…For functions with finite-dimensional codomains, the problem has been studied by Clarke [3], Craven [5], Minami [13], Reiland [22], Bhatia and Jain [1], Lee [11], Giorgi and Guerraggio [7], Liu [12], Mishra [14], Mishra and Mukherjee [16], Kim [10], and others. The infinite-dimensional case was considered by El Abdouni and Thibault [6], Coladas et al [4], and by Brandao et al [2]. Brandao et al [2] studied multiobjective mathematical programming with nondifferentiable strongly compact Lipschitz functions defined on general Banach spaces.…”