Journal ArticleDOI
Stability and regular points of inequality systems
TLDR
In this paper, a general study of regular points of Lipschitz and strictly differentiable mappings with applications to tangent cone analysis, inversion theorems, perturbed optimization problems, and higher-order conditions is presented.Abstract:
We undertake a general study of regular points of Lipschitz and strictly differentiable mappings with applications to tangent cone analysis, inversion theorems, perturbed optimization problems, and higher-order conditionsread more
Citations
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Convex analysis and nonlinear optimization : theory and examples
TL;DR: In this paper, the Karush-Kuhn-Tucker Theorem and Fenchel duality were used for infinite versus finite dimensions, with a list of results and notation.
Book
Implicit Functions and Solution Mappings
TL;DR: In this article, the authors provide a reference on the topic and a unified collection of a number of results which are currently scattered throughout the literature, including implicit mappings defined by relations other than equations.
Journal ArticleDOI
Error bounds in mathematical programming
TL;DR: This paper gives a comprehensive, state-of-the-art survey of the extensive theory and rich applications of error bounds for inequality and optimization systems and solution sets of equilibrium problems.
Book
Implicit Functions and Solution Mappings: A View from Variational Analysis
TL;DR: In this paper, the authors define implicit functions defined implicitly by equations, and derive regularity properties of set-valued solution mappings through generalized derivatives, and apply them in Numerical Variational Analysis.
Journal ArticleDOI
Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions
TL;DR: In this article, the authors consider some basic properties of nonsmooth and set-valued mappings (multifunctions) connected with open and inverse mapping principles, distance estimates to the level sets (metric regularity), and a locally Lipschitzian behavior.
References
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Book
Optimization and nonsmooth analysis
TL;DR: The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.
Book
Principles of mathematical analysis
TL;DR: The real and complex number system as discussed by the authors is a real number system where the real number is defined by a real function and the complex number is represented by a complex field of functions.
Book
Optimization by Vector Space Methods
TL;DR: This book shows engineers how to use optimization theory to solve complex problems with a minimum of mathematics and unifies the large field of optimization with a few geometric principles.
Book
Convex analysis and variational problems
Ivar Ekeland,Roger Téman +1 more
TL;DR: In this article, the authors consider non-convex variational problems with a priori estimate in convex programming and show that they can be solved by the minimax theorem.
Journal ArticleDOI
On the variational principle
TL;DR: The variational principle states that if a differentiable function F has a finite lower bound (although it need not attain it), then, for every E > 0, there exists some point u( where 11 F'(uJj* < l, i.e., its derivative can be made arbitrarily small as discussed by the authors.