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Krzysztof E. Rutkowski

Publications and source records attributed to Krzysztof E. Rutkowski.

11 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.

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arXiv2024

Numerical methods for solving the linearized model of a hinged-free reduced plate arising in flow structure interactions

The problem of partially hinged and partially free rectangular plate that aims to represent a suspension bridge subject to some external forces (for example the wind) is considered in order to model and simulate the unstable end behavior. Such a problem can be modeled by a plate evolution equation, which is nonlinear with a nonlocal stretching effect in the spanwise direction. The external forces are periodic in time and cause the vortex shedding on the structure (on the surface of the plate) and thus it may cause damage to the material. Numerical study of the behavior of steady state solutions for different values of the force velocity are provided with two finite element methods of different type.

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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.

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arXiv2021

Dynamical system related to primal-dual splitting projection methods

We introduce a dynamical system to the problem of finding zeros of the sum of two maximally monotone operators. We investigate the existence, uniqueness and extendability of solutions to this dynamical system in a Hilbert space. We prove that the trajectories of the proposed dynamical system converge strongly to a primal-dual solution of the considered problem. Under explicit time discretization of the dynamical system we obtain the best approximation algorithm for solving coupled monotone inclusion problem.

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arXiv2019

On Lipschitz continuity of projections onto polyhedral moving sets

In Hilbert space setting we prove local lipchitzness of projections onto parametric polyhedral sets represented as solutions to systems of inequalities and equations with parameters appearing both in left-hand-sides and right-hand-sides of the constraints. In deriving main results we assume that data are locally Lipschitz functions of parameter and the relaxed constant rank constraint qualification condition is satisfied.

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arXiv2018

On Lipschitz-like property for polyhedral moving sets

We give sufficient conditions for Lipschitz-likeness of a class of polyhedral set-valued mappings in Hilbert spaces based on Relaxed Constant Rank Constraint Qualification (RCRCQ) proposed recently by Minchenko and Stakhovsky. To this aim we prove the R-regularity of the considered set-valued mapping and correct the respective proof given by these authors.

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arXiv2018

Proximal primal-dual best approximation algorithm with memory

We propose a new modified primal-dual proximal best approximation method for solving convex not necessarily differentiable optimization problems. The novelty of the method relies on introducing memory by taking into account iterates computed in previous steps in the formulas defining current iterate. To this end we consider projections onto intersections of halfspaces generated on the basis of the current as well as the previous iterates. To calculate these projections we are using recently obtained closed-form expressions for projectors onto polyhedral sets. The resulting algorithm with memory inherits strong convergence properties of the original best approximation proximal primal-dual algorithm. Additionally, we compare our algorithm with the original (non-inertial) one with the help of the so called attraction property defined below. Extensive numerical experimental results on image reconstruction problems illustrate the advantages of including memory into the original algorithm.

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arXiv2017

Closed-form expressions for projectors onto polyhedral sets in Hilbert spaces

We provide formulas for projectors onto a polyhedral set, i.e. the intersection of a finite number of halfspaces. To this aim we formulate the problem of finding the projection as a convex optimization problem and we solve explicitly sufficient and necessary optimality conditions. This approach has already been successfully applied in deriving formulas for projection onto the intersection of two halfspaces. We also discuss possible generalizations to Banach spaces.

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