Generic Well-Posedness of Minimization Problems with Constraints

2010 ◽  
pp. 311-347
Author(s):  
Alexander J. Zaslavski
Keyword(s):  
Well Posedness ◽  
Minimization Problems

scholarly journals Generic well-posedness in minimization problems

2005 ◽  
Vol 2005 (4) ◽  
pp. 343-360 ◽  
Author(s):  
A. Ioffe ◽  
R. E. Lucchetti
Keyword(s):  
Uniform Convergence ◽  
Well Posedness ◽  
Minimization Problems ◽  
Bounded Sets ◽  
Well Posed ◽  
Class Of Functions

The goal of this paper is to provide an overview of results concerning, roughly speaking, the following issue: given a (topologized) class of minimum problems, “how many” of them are well-posed? We will consider several ways to define the concept of “how many,” and also several types of well-posedness concepts. We will concentrate our attention on results related to uniform convergence on bounded sets, or similar convergence notions, as far as the topology on the class of functions under investigation is concerned.

scholarly journals Well-Posedness and Porosity for Symmetric Optimization Problems

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1253
Author(s):  
Alexander J. Zaslavski
Keyword(s):  
Metric Space ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Complete Metric Space ◽  
Well Posedness ◽  
Porous Set ◽  
Minimization Problems ◽  
Symmetric Optimization ◽  
Lower Semi ◽  
Well Posed

In the present work, we investigate a collection of symmetric minimization problems, which is identified with a complete metric space of lower semi-continuous and bounded from below functions. In our recent paper, we showed that for a generic objective function, the corresponding symmetric optimization problem possesses two solutions. In this paper, we strengthen this result using a porosity notion. We investigate the collection of all functions such that the corresponding optimization problem is well-posed and prove that its complement is a σ-porous set.

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

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