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The complex gradient inequality with parameter
 submitted; 14 MACIEJ P. DENKOWSKI
, 2014
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EFFECTIVE LOJASIEWICZ GRADIENT INEQUALITY FOR POLYNOMIALS
"... Abstract. Let f: R n → R be a polynomial function of degree d with f(0) = 0 and ∇f(0) = 0. Lojasiewicz’s gradient inequality states there exist C> 0 and ρ ∈ (0, 1) such that ∇f  ≥ Cf  ρ in a neighbourhood of the origin. We prove that the smallest of such exponents ρ is not greater than 1 − ..."
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Abstract. Let f: R n → R be a polynomial function of degree d with f(0) = 0 and ∇f(0) = 0. Lojasiewicz’s gradient inequality states there exist C> 0 and ρ ∈ (0, 1) such that ∇f  ≥ Cf  ρ in a neighbourhood of the origin. We prove that the smallest of such exponents ρ is not greater than 1
The LojasiewiczSimon gradient inequality on Hilbert spaces
 Proceedings of the 5 th EuropeanMaghrebian Workshop on Semigroup Theory, Evolution Equations, and Applications
"... Abstract. In this article we study the LojasiewiczSimon gradient inequality for energy functionals defined on Hilbert spaces, using the socalled critical manifold. We indicate applications to partial differential equations. 1. ..."
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Cited by 2 (0 self)
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Abstract. In this article we study the LojasiewiczSimon gradient inequality for energy functionals defined on Hilbert spaces, using the socalled critical manifold. We indicate applications to partial differential equations. 1.
A Gradient Inequality at Infinity for Tame Functions
 Rev. Mat. Complut
"... Abstract. Let f be a C 1 function defined over R n and definable in a given ominimal structure M expanding the real field. We prove here a gradientlike inequality at infinity in a neighbourhood of an asymptotic critical value c. When f is C 2 we use this inequality to discuss the trivialisation by ..."
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Cited by 1 (1 self)
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Abstract. Let f be a C 1 function defined over R n and definable in a given ominimal structure M expanding the real field. We prove here a gradientlike inequality at infinity in a neighbourhood of an asymptotic critical value c. When f is C 2 we use this inequality to discuss the trivialisation
SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
, 2002
"... Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first deriv ..."
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Cited by 597 (24 self)
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Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first
APPLICATIONS OF THE LOJASIEWICZSIMON GRADIENT INEQUALITY TO GRADIENTLIKE EVOLUTION EQUATIONS
"... We prove convergence to equilibrium of global and bounded solutions of gradientlike evolution equations. Our abstract results are illustrated by several examples in finite and infinite dimensions. ..."
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Cited by 5 (2 self)
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We prove convergence to equilibrium of global and bounded solutions of gradientlike evolution equations. Our abstract results are illustrated by several examples in finite and infinite dimensions.
2 Equivalent Harnack and Gradient Inequalities for Pointwise Curvature Lower Bound ∗
, 2014
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Skill Biased Technological Change and Rising Wage Inequality: Some Problems and Puzzles
 NATIONAL BUREAU OF ECONOMIC RESEARCH
, 2002
"... The recent rise in wage inequality is usually attributed to skillbiased technical change (SBTC), associated with new computer technologies. We review the evidence for this hypothesis, focusing on the implications of SBTC for overall wage inequality and for changes in wage differentials between grou ..."
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Cited by 308 (4 self)
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groups. A key problem for the SBTC hypothesis is that wage inequality stabilized in the 1990s despite continuing advances in computer technology; SBTC also fails to explain the evolution of other dimensions of wage inequality, including the gender and racial wage gaps and the age gradient in the return
Transport inequalities, gradient estimates, entropy and Ricci curvature
 Comm. Pure Appl. Math
"... Abstract. We present various characterizations of uniform lower bounds for the Ricci curvature of a smooth Riemannian manifold M in terms of convexity properties of the entropy (considered as a function on the space of probability measures on M ) as well as in terms of transportation inequalities f ..."
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Cited by 131 (3 self)
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Abstract. We present various characterizations of uniform lower bounds for the Ricci curvature of a smooth Riemannian manifold M in terms of convexity properties of the entropy (considered as a function on the space of probability measures on M ) as well as in terms of transportation inequalities
Gradient and Harnack inequalities on noncompact manifolds with boundary
 Pacific Journal of Math
"... By using the reflecting diffusion process and a conformal change of metric, a generalized maximum principle is established for (unbounded) timespace functions on a class of noncompact Riemannian manifolds with (nonconvex) boundary. As applications, Li–Yautype gradient and Harnack inequalities are ..."
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Cited by 6 (2 self)
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By using the reflecting diffusion process and a conformal change of metric, a generalized maximum principle is established for (unbounded) timespace functions on a class of noncompact Riemannian manifolds with (nonconvex) boundary. As applications, Li–Yautype gradient and Harnack inequalities
Results 1  10
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704