Complete Characterizations of Tilt Stability in Nonlinear Programming under Weakest Qualification Conditions
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In this article, the tilt stability of local minimizers for nonlinear programs with equality and inequality constraints in finite dimensions described by two continuous 2-dimensional 2-D planes is studied.Abstract:
This paper is devoted to the study of tilt stability of local minimizers for classical nonlinear programs with equality and inequality constraints in finite dimensions described by twice continuous...read more
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On Computation of Generalized Derivatives of the Normal-Cone Mapping and their Applications
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A robust multigrid method for Isogeometric Analysis in two dimensions using boundary correction
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Critical multipliers in variational systems via second-order generalized differentiation
TL;DR: In this article, it is shown that noncriticality is equivalent to a certain calmness property of a perturbed variational system and that critical multipliers can be ruled out by full stability of local minimizers in problems of composite optimization.
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Error bounds for parametric polynomial systems with applications to higher-order stability analysis and convergence rates
TL;DR: In this article, a far-going extension of the Łojasiewicz gradient inequality to the general nonsmooth class of supremum marginal functions as well as higher-order (Holder type) local error bounds with explicitly calculated exponents is presented, which can be viewed as solution sets to problems of generalized semi-infinite programming with polynomial data.
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Error Bounds for Parametric Polynomial Systems with Applications to Higher-Order Stability Analysis and Convergence Rates
TL;DR: In this article, a far-going extension of the L ojasiewicz gradient inequality to the general nonsmooth class of supremum marginal functions as well as higher-order (H\"older type) local error bounds with explicitly calculated exponents is presented.
References
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Strongly Regular Generalized Equations
TL;DR: A regularity condition is introduced for generalized equations and it is shown to be in a certain sense the weakest possible condition under which the stated properties will hold.
Perturbation Analysis Of Optimization Problems
TL;DR: The perturbation analysis of optimization problems is universally compatible with any devices to read and will help you to enjoy a good book with a cup of tea in the afternoon instead of facing with some malicious virus inside their computer.
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Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications (Nonconvex Optimization and Its Applications)
Diethard Klatte,Bernd Kummer +1 more
TL;DR: In this article, a unified theory of Lipschitzian critical points in optimization and other variational problems, with relations to reformulations by penalty, barrier and NCP functions, is presented, along with an analysis of generalized Newton methods based on linear and nonlinear approximations.
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Calmness of constraint systems with applications
René Henrion,Jiří V. Outrata +1 more
TL;DR: The obtained conditions enable the detection of calmness in a number of situations, where the standard criteria do not work, and their application in the framework of generalized differential calculus is explained and illustrated.