Strict Efficiency in Vector Optimization

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Optimality Conditions in Differentiable Vector Optimization via Second-Order Tangent Sets (2004, methodology): “We have that every strict local minimum of order m is also of order j, for all j ≥ m, and every strict local minimum of order m is a local minimum, that is, Strl(m, f, M) ⊂ LMin( f, M) (see [ 12 ]).”
First order optimality conditions in vector optimization involving stable functions (2008, background): “8 (part (d) implies (b)) in [9], where the function f is Fréchet differentiable.”
Optimality Conditions for Nonsmooth Multiobjective Optimization Using Hadamard Directional Derivatives (2007, background): “[21, 28, 38 ]) A feasible point x0 of problem (P) is termed a local firm efficient point of order α> 0 of (P) if there are h> 0 and a neighborhood U of x0 such that, with ϕ given in (2),”
Higher-order necessary and sufficient conditions for strict local pareto minima in terms of Studniarski's derivatives (2008, background): “Recently, the notion of strict local minimum of order m for single-objective optimization problems is extended to multiobjective programing problems by Jimenez 8 .”