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534
Inverse and implicit function theorems for Hdifferentiable and semismooth functions
, 2000
"... With utmost pleasure, I dedicate this article to my teacher, mentor, and friend Olvi Mangasarian on the occasion of his 70th birthday In this article, we prove inverse and implicit function theorems for Hdifferentiable functions, thereby giving a unified treatment of such theorems for C1functions, ..."
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Cited by 17 (1 self)
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, PC1functions, and for locally Lipschitzian functions. We also derive inverse and implicit function theorems for semismooth functions.
Keywords Nonlinear Equations · Semismooth Functions · Newton’s Method · Nonlinear Complementarity Problems
"... Abstract We discuss local convergence of Newton’s method to a singular solution x ∗ of the nonlinear equations F (x) = 0, for F: IR n → IR n. It is shown that an existing proof of Griewank, concerning linear convergence to a singular solution x ∗ from a starlike domain around x ∗ for F twice Lipsch ..."
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solution by overrelaxing every second Newton step. These results are applied to a nonlinearequations reformulation of the nonlinear complementarity problem (NCP) whose derivative is strongly semismooth when the function f arising in the NCP is sufficiently smooth. Conditions on f are derived that ensure
Semismooth Matrix Valued Functions
, 1999
"... . Matrix valued functions play an important role in the development of algorithms for semidefinite programming problems. This paper studies generalized di#erential properties of such functions related to nonsmoothsmoothing Newton methods. The first part of this paper discusses basic properties such ..."
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Cited by 62 (26 self)
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such as the generalized derivative, Rademacher's theorem, Bderivative, directional derivative, and semismoothness. The second part shows that the matrix absolutevalue function, the matrix semidefiniteprojection function, and the matrix projective residual function are strongly semismooth. Keywords: Matrix
Semismooth Equations ∗
"... [Article] Hybrid Newtontype method for a class of semismooth equations ..."
Radiality and semismoothness
 Control and Cybernetics
"... Abstract: We provide sufficient conditions for radiality and semismoothness. In general Banach spaces, we show that calmness ensures Diniradiality as well as Diniconvexity of solution set to inequality systems. In finite dimensional spaces, we introduce the concept of Clarkeradiality and semismoo ..."
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Cited by 2 (0 self)
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radiality and semismoothness of order m and show that each subanalytic set satisfies these properties. Similar properties are obtained for locally Lipschitzian subanalytic functions.
SEMISMOOTH METHODS FOR LINEAR AND NONLINEAR
, 2006
"... The optimality conditions of a nonlinear secondorder cone program can be reformulated as a nonsmooth system of equations using a projection mapping. This allows the application of nonsmooth Newton methods for the solution of the nonlinear secondorder cone program. Conditions for the local quadra ..."
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: Linear secondorder cone program, nonlinear secondorder cone program, semismooth function, nonsmooth Newton method, quadratic convergence
Tame functions are semismooth
 hal00777707, version 1  17
, 2013
"... Abstract Superlinear convergence of the Newton method for nonsmooth equations requires a “semismoothness ” assumption. In this work we prove that locally Lipschitz functions definable in an ominimal structure (in particular semialgebraic or globally subanalytic functions) are semismooth. Semialgebr ..."
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Cited by 16 (7 self)
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Abstract Superlinear convergence of the Newton method for nonsmooth equations requires a “semismoothness ” assumption. In this work we prove that locally Lipschitz functions definable in an ominimal structure (in particular semialgebraic or globally subanalytic functions) are semismooth
Semismoothness Of Spectral Functions
"... Any spectral function can be written as a composition of a symmetric function f: IRn 7! IR and the eigenvalue function *(*) : S 7! IRn, often denoted by (f ffi *), where S ..."
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Cited by 7 (0 self)
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Any spectral function can be written as a composition of a symmetric function f: IRn 7! IR and the eigenvalue function *(*) : S 7! IRn, often denoted by (f ffi *), where S
Asymptotic semismoothness probabilities
 Mathematics of computation
, 1996
"... Abstract. We call an integer semismooth with respect to y and z if each of its prime factors is ≤ y, and all but one are ≤ z. Such numbers are useful in various factoring algorithms, including the quadratic sieve. Let G(α, β)bethe asymptotic probability that a random integer n is semismooth with res ..."
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Cited by 26 (2 self)
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Abstract. We call an integer semismooth with respect to y and z if each of its prime factors is ≤ y, and all but one are ≤ z. Such numbers are useful in various factoring algorithms, including the quadratic sieve. Let G(α, β)bethe asymptotic probability that a random integer n is semismooth
Secant Methods for Semismooth Equations
 Numerische Mathematik
, 1998
"... Some generalizations of the secant method to semismooth equations are presented. In the onedimensional case the superlinear convergence of the classical secant method for general semismooth equations is proved. Moreover a new quadratically convergent method is proposed that requires two function va ..."
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Cited by 5 (1 self)
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Some generalizations of the secant method to semismooth equations are presented. In the onedimensional case the superlinear convergence of the classical secant method for general semismooth equations is proved. Moreover a new quadratically convergent method is proposed that requires two function
Results 1  10
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534