Displaying similar documents to “Well-posed minimum problems for preorders”

Epigraphical analysis

H. Attouch, R. J.-B. Wets (1989)

Annales de l'I.H.P. Analyse non linéaire

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Strong-weak Stackelberg Problems in Finite Dimensional Spaces

Aboussoror, Abdelmalek, Loridan, Pierre (1995)

Serdica Mathematical Journal

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We are concerned with two-level optimization problems called strongweak Stackelberg problems, generalizing the class of Stackelberg problems in the strong and weak sense. In order to handle the fact that the considered two-level optimization problems may fail to have a solution under mild assumptions, we consider a regularization involving ε-approximate optimal solutions in the lower level problems. We prove the existence of optimal solutions for such regularized problems and present...

A note on Minty type vector variational inequalities

Giovanni P. Crespi, Ivan Ginchev, Matteo Rocca (2005)

RAIRO - Operations Research - Recherche Opérationnelle

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The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space Y are...

Porosity and Variational Principles

Marchini, Elsa (2002)

Serdica Mathematical Journal

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We prove that in some classes of optimization problems, like lower semicontinuous functions which are bounded from below, lower semi-continuous or continuous functions which are bounded below by a coercive function and quasi-convex continuous functions with the topology of the uniform convergence, the complement of the set of well-posed problems is σ-porous. These results are obtained as realization of a theorem extending a variational principle of Ioffe-Zaslavski.

The concentration-compactness principle in the calculus of variations. The limit case, Part II.

Pierre-Louis Lions (1985)

Revista Matemática Iberoamericana

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This paper is the second part of a work devoted to the study of variational problems (with constraints) in functional spaces defined on domains presenting some (local) form of invariance by a non-compact group of transformations like the dilations in R. This contains for example the class of problems associated with the determination of extremal functions in inequalities like Sobolev inequalities, convolution or trace inequalities... We show how the concentration-compactness principle...

Inferior Limit, Superior Limit and Convergence of Sequences of Extended Real Numbers

Hiroshi Yamazaki, Noboru Endou, Yasunari Shidama, Hiroyuki Okazaki (2007)

Formalized Mathematics

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In this article, we extended properties of sequences of real numbers to sequences of extended real numbers. We also introduced basic properties of the inferior limit, superior limit and convergence of sequences of extended real numbers.