arXiv subjects

Rongzhen Lyu

Publications and source records attributed to Rongzhen Lyu.

2 recordsLinked to original sources

arXiv2024

Alternative theorem for sequences of functions and applications to optimisation

We present a new alternative theorems for sequences of functions. As applications, we extend recent results in the literature related to first-order necessary conditions for optimality problems. Our contributions involve extending well-known results, previously established for a finite number of inequality constraints to a countable number of inequality constraints. This extension is achieved using the Dini differentiability concept which is more general than Fréchet or Gâteaux differentiability. We will illustrate our results by giving examples of optimisation problems with a finite or countable number of inequality constraints where the functions are not Gateaux-differentiable but only upper Dini-differentiable.

math.OC↗

arXiv2023

Multiplier rules for Dini-derivatives in a topological vector space

We provide new results of first-order necessary conditions of optimality problem in the form of John's theorem and in the form of Karush-Kuhn-Tucker's theorem. We establish our result in a topological vector space for problems with inequality constraints and in a Banach space for problems with equality and inequality constraints. Our contributions consist in the extension of the results known for the Fréchet and Gateaux-differentiable functions as well as for the Clarke's subdifferential of Lipschitz functions, to the more general Dini-differentiable functions. As consequences, we extend the result of B.H. Pourciau in \cite[Theorem 6, p. 445]{Po} from the convexity to the {\it "Dini-pseudoconvexity"}.

math.OC↗