Displaying similar documents to “On existence of solutions to degenerate nonlinear optimization problems”

Second order optimality conditions for differentiable multiobjective problems

Giancarlo Bigi, Marco Castellani (2010)

RAIRO - Operations Research

Similarity:

A second order optimality condition for multiobjective optimization with a set constraint is developed; this condition is expressed as the impossibility of nonhomogeneous linear systems. When the constraint is given in terms of inequalities and equalities, it can be turned into a John type multipliers rule, using a nonhomogeneous Motzkin Theorem of the Alternative. Adding weak second order regularity assumptions, Karush, Kuhn-Tucker type conditions are therefore deduced. ...

On the normal variations of a domain

D. Bresch, J. Simon (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In domain optimization problems, normal variations of a reference domain are frequently used. We prove that such variations do not preserve the regularity of the domain. More precisely, we give a bounded domain which boundary is m times differentiable and a scalar variation which is infinitely differentiable such that the deformed boundary is only m-1 times differentiable. We prove in addition that the only normal variations which preserve the regularity are those with constant magnitude....

Generalization of p-regularity notion and tangent cone description in the singular case

Wiesław Grzegorczyk, Beata Medak, Alexey A. Tret’yakov (2012)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions. ...

Saddle points criteria via a second order η -approximation approach for nonlinear mathematical programming involving second order invex functions

Tadeusz Antczak (2011)

Kybernetika

Similarity:

In this paper, by using the second order η -approximation method introduced by Antczak [3], new saddle point results are obtained for a nonlinear mathematical programming problem involving second order invex functions with respect to the same function η . Moreover, a second order η -saddle point and a second order η -Lagrange function are defined for the so-called second order η -approximated optimization problem constructed in this method. Then, the equivalence between an optimal solution...

Accurate WKB Approximation for a 1D Problem with Low Regularity

Nier, F. (2008)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: 34L40, 65L10, 65Z05, 81Q20. This article is concerned with the analysis of the WKB expansion in a classically forbidden region for a one dimensional boundary value Schrodinger equation with a non smooth potential. The assumed regularity of the potential is the one coming from a non linear problem and seems to be the critical one for which a good exponential decay estimate can be proved for the first remainder term. The treatment of...