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Variational analysis and generalized differentiation I : basic theory
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The article was published on 2006-01-01. It has received 1528 citations till now. The article focuses on the topics: Variational analysis & Calculus of variations.read more
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Proximal alternating linearized minimization for nonconvex and nonsmooth problems
TL;DR: A self-contained convergence analysis framework is derived and it is established that each bounded sequence generated by PALM globally converges to a critical point.
Journal ArticleDOI
Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods
TL;DR: This work proves an abstract convergence result for descent methods satisfying a sufficient-decrease assumption, and allowing a relative error tolerance, that guarantees the convergence of bounded sequences under the assumption that the function f satisfies the Kurdyka–Łojasiewicz inequality.
Journal ArticleDOI
Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality
TL;DR: In this paper, the convergence properties of an alternating proximal minimization algorithm for nonconvex structured functions of the type: L(x,y)=f(x)+Q(x+,y)+g(y), where f and g are proper lower semicontinuous functions, defined on Euclidean spaces, and Q is a smooth function that couples the variables x and y.
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.
Book
Convex Functions: Constructions, Characterizations and Counterexamples
TL;DR: Convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied as mentioned in this paper, and is an important tool in optimization, mathematical programming and game theory.