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Disjunctive Optimization: Critical Point Theory [PDF]
Journal of Optimization Theory and Applications, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Oliver Stein +2 more
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SIAM Journal on Optimization, 2009
We study mathematical programs with complementarity constraints (MPCC) from a topological point of view. Special focus will be on C-stationary points. Under the linear independence constraint qualification (LICQ) we derive an equivariant Morse lemma at nondegenerate C-stationary points.
H. Th. Jongen +2 more
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We study mathematical programs with complementarity constraints (MPCC) from a topological point of view. Special focus will be on C-stationary points. Under the linear independence constraint qualification (LICQ) we derive an equivariant Morse lemma at nondegenerate C-stationary points.
H. Th. Jongen +2 more
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, 1999 Many nonlinear problems can be reduced to the form Many nonlinear problems can be reduced to the form $$G'(u) = 0,$$ (1.1.1) where G is a C1-functional on a Banach space E. In this case the problems can be attacked by specialized, important techniques which can produce results where other methods fail.
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2019
Critical point theory deals with variational problems and so it can be argued that it is as old as calculus. Nevertheless, in its modern form, critical point theory has its roots in the so-called “Dirichlet principle”.
Nikolaos S. Papageorgiou +2 more
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Critical point theory deals with variational problems and so it can be argued that it is as old as calculus. Nevertheless, in its modern form, critical point theory has its roots in the so-called “Dirichlet principle”.
Nikolaos S. Papageorgiou +2 more
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Nonsmooth critical point theory and applications
Nonlinear Analysis: Theory, Methods & Applications, 1997The author surveys recent developments in critical point theory for (not necessarily continuous) functions \(f \colon X \to \overline{\mathbb{R}}\) where \(X\) is a metric space. First he discusses the weak slope \(| df| (u) \in [0,\infty)\) which is defined if \(f(u) \in \mathbb{R}\). This concept is well suited for critical point theory provided that
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The Critical Point: Theory and Experiment
High Temperature, 2001It is demonstrated that the Gibbs concept of the critical state and the equations for the critical point formulated by him make it possible to provide a complete description the peculiarities of the behavior and properties of matter at the critical point.
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Theory of the Critical Point of 4He
1990We do not have yet a microscopic global theory of the thermodynamic properties of 4He in the normal phase, inclusive of the region of the critical point. At a very simple level the effect of the attractive part of the interatomic forces has been considered1 in a perturbative way starting from the properties of quantum hard spheres.
K. J. Runge, L. Reatto, A. Meroni
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Nonsmooth Critical Point Theory
1999The aim of this chapter is to present general results, many of them belonging to the authors, that can be applied to locally Lipschitz functionals, possibly invariant under a compact Lie group of linear isometries. The nonsmooth critical point theory in the locally Lipschitz case originates in the work of Chang [4].
Dumitru Motreanu +1 more
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1993
In the study of nonminimum critical points, a basic method is the so-called minimax principle. In this chapter we study the connections between Morse theory and a variety of concrete versions of the minimax principle. We point out that the minimax principle for relative homology classes is particularly suitable for Morse theory because certain critical
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In the study of nonminimum critical points, a basic method is the so-called minimax principle. In this chapter we study the connections between Morse theory and a variety of concrete versions of the minimax principle. We point out that the minimax principle for relative homology classes is particularly suitable for Morse theory because certain critical
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Critical Points and Morse Theory
1997In this chapter we introduce Morse theory, a systematic way of studying certain features of smooth functions on manifolds. We will primarily consider surfaces and three-manifolds, because the main applications of Morse theory in computer geometry are concentrated in these dimensions.
Tosiyasu L. Kinii, Anatolij T. Fomenko
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