Journal ArticleDOI
Characterizations of full stability in constrained optimization
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TLDR
Based on second-order generalized differential tools of variational anal- ysis, necessary and sufficient conditions are obtained for fully stable local minimizers in general classes of constrained optimization problems, including problems of composite optimization, mathemati- cal programs with polyhedral constraints, as well as problems of extended and classical nonlinear programming with twice continuously differentiable data.Abstract:
This paper is mainly devoted to the study of the so-called full Lipschitzian stability of local solutions to finite-dimensional parameterized problems of constrained optimization, which has been well recognized as a very important property from the viewpoints of both optimization theory and its applications. Based on second-order generalized differential tools of variational anal- ysis, we obtain necessary and sufficient conditions for fully stable local minimizers in general classes of constrained optimization problems, including problems of composite optimization, mathemati- cal programs with polyhedral constraints, as well as problems of extended and classical nonlinear programming with twice continuously differentiable data.read more
Citations
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Journal ArticleDOI
New fractional error bounds for polynomial systems with applications to Hölderian stability in optimization and spectral theory of tensors
TL;DR: New fractional error bounds for polynomial systems with exponents explicitly determined by the dimension of the underlying space and the number/degree of the involved polynomials are derived.
Posted Content
Second-order growth, tilt stability, and metric regularity of the subdifferential
TL;DR: In this paper, the authors established new relationships between second-order growth conditions on functions, the basic properties of metric regularity and subregularity of the limiting subdifferential, tilt-stability of local minimizers, and positive-definiteness/semidefiniteness properties of the second order Hessian.
Journal ArticleDOI
Full Lipschitzian and Hölderian Stability in Optimization with Applications to Mathematical Programming and Optimal Control
TL;DR: A systematic study of full stability in general optimization models including its conventional Lipschitzian version as well as the new Holderian version, both of which derive various characterizations.
Journal ArticleDOI
Complete Characterizations of Tilt Stability in Nonlinear Programming under Weakest Qualification Conditions
TL;DR: 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.
Journal ArticleDOI
Second-order characterizations of tilt stability with applications to nonlinear programming
TL;DR: A new approach to tilt stability is developed, which allows for not only qualitative but also quantitative characterizations of tilt-stable minimizers with calculating the corresponding moduli under new second-order qualification and optimality conditions.
References
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Finite-Dimensional Variational Inequalities and Complementarity Problems
TL;DR: Newton Methods for Nonsmooth Equations as mentioned in this paper and global methods for nonsmooth equations were used to solve the Complementarity problem in the context of non-complementarity problems.
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Perturbation Analysis of Optimization Problems
TL;DR: It is shown here how the model derived recently in [Bouchut-Boyaval, M3AS (23) 2013] can be modified for flows on rugous topographies varying around an inclined plane.
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Variational Analysis and Generalized Differentiation II
TL;DR: In this article, the authors propose a constrained optimization and equilibrium approach for optimal control of evolution systems in Banach spaces. And they apply this approach to distributed systems in economics applications.
Journal ArticleDOI
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.