arXiv subjects

Krzysztof W. Leśniewski

Publications and source records attributed to Krzysztof W. Leśniewski.

3 recordsLinked to original sources

arXiv2024

Mangasarian-Fromovitz-type constraint qualification and optimality conditions for smooth infinite programming problems

We introduce a constraint qualification condition (GPMFCQ) for smooth infinite programming problems, where the nonlinear operator defining the equality constraints has nonsurjective derivative at the local minimum. The condition is a generalization of PMFCQ introduced by Morduhovich and Nghia. We prove the existence of Lagrange multipliers by using either Hurwicz set or Nonlinear Farkas Minkowski condition.

math.OC↗

arXiv2022

Abadie condition for infinite programming problems under Relaxed Constant Rank Constraint Qualification Plus

We consider infinite programming problems with constraint sets defined by systems of infinite number of inequalities and equations given by continuously differentiable functions defined on Banach spaces. In the approach proposed here we represent these systems with the help of coefficients in a given Schauder basis. We prove the Abadie condition under the new infinite-dimensional Relaxed Constant Rank Constraint Qualification Plus and we discuss the existence of Lagrange multipliers. The main tools are: Rank Theorem and Ljusternik Theorem.

math.AT↗

arXiv2020

On tangent cone to systems of inequalities and equations in Banach spaces under relaxed constant rank condition

Under the relaxed constant rank condition, introduced by Minchenko and Stakhovski, we prove that the linearized cone is contained in the tangent cone (Abadie condition) for sets represented as solution sets to systems of finite numbers of inequalities and equations given by continuously differentiable functions defined on Banach spaces.

math.OC↗