From Scalar to Vector Optimization

By Ivan Ginchev, A. Guerraggio, Matteo Rocca. 2006

108 citations recorded by the source corpus.

AbstractInitially, second-order necessary optimality conditions and sufficient optimality conditions in terms of Hadamard type derivatives for the unconstrained scalar optimization problem ϕ(x) → min, x ∈ ℝm, are given. These conditions work with arbitrary functions ϕ: ℝm → ℝ, but they show inconsistency with the classical derivatives. This is a base to pose the question whether the formulated optimality conditions remain true when the “inconsistent” Hadamard derivatives are replaced with the “consistent” Dini derivatives. It is shown that the answer is affirmative if ϕ is of class $$\mathcal{C}^{1,1}$$ (i.e., differentiable with locally Lipschitz derivative).Further, considering $$\mathcal{C}^{1,1}$$ functions, the discussion is raised to unconstrained vector optimization problems. Using the so called “oriented distance” from a point to a set, we generalize to an arbitrary ordering cone some second-order necessary conditions and sufficient conditions given by Liu, Neittaanmaki, Krizek for a polyhedral cone. Furthermore, we show that the conditions obtained are sufficient not only for efficiency but also for strict efficiency.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f549e1e8224cfefad21790fa29d0c7df03641100

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

  1. Phan Nguyen Quoc Khanh
  2. Nguyen Dinh Tuan
  3. Lam Quoc Anh

In Numerical Analysis

  1. Phan Nguyen Quoc Khanh
  2. Nguyen Dinh Tuan

Citations in the corpus