8 papers · 1 filter
Mangasarian-Fromovitz-type constraint qualification and optimality conditions for smooth infinite programming problems
Ewa M. Bednarczuk, Krzysztof W. Leśniewski, Krzysztof E. Rutkowski
We introduce a constraint qualification condition (GPMFCQ) for smooth infinite programming problems, where the nonlinear operator defining the equality constraints has nonsurjectiv…
Outer Approximation Scheme for Weakly Convex Constrained Optimization Problems
Ewa M. Bednarczuk, Giovanni Bruccola, Jean-Christophe Pesquet +1
Outer approximation methods have long been employed to tackle a variety of optimization problems, including linear programming, in the 1960s, and continue to be effective for solvi…
On Lipschitz continuity of projections onto polyhedral moving sets
Ewa M. Bednarczuk, Krzysztof E. Rutkowski
In Hilbert space setting we prove local lipchitzness of projections onto parametric polyhedral sets represented as solutions to systems of inequalities and equations with parameter…
On Lipschitz-like continuity of a class of set-valued mappings
Ewa M. Bednarczuk, Leonid I. Minchenko, Krzysztof E. Rutkowski
We study set-valued mappings defined by solution sets of parametric systems of equalities and inequalities. We prove Lipschitz-like continuity of these mappings under relaxed const…
On tangent cone to systems of inequalities and equations in Banach spaces under relaxed constant rank condition
Ewa M. Bednarczuk, Krzysztof W. Leśniewski, Krzysztof E. Rutkowski
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 re…
On Lipschitz-like property for polyhedral moving sets
Ewa M. Bednarczuk, Krzysztof E. Rutkowski
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)…
Proximal primal-dual best approximation algorithm with memory
Ewa M. Bednarczuk, Anna Jezierska, Krzysztof E. Rutkowski
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 o…
Closed-form expressions for projectors onto polyhedral sets in Hilbert spaces
Krzysztof E. Rutkowski
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…