The Kurdyka–Łojasiewicz Inequality as Regularity Condition
From MaRDI portal
Publication:3299973
DOI10.1007/978-981-15-1592-7_12zbMath1443.35186arXiv1905.10177OpenAlexW3005353946MaRDI QIDQ3299973
Daniel Gerth, Stefan Kindermann
Publication date: 27 July 2020
Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1905.10177
Nonconvex programming, global optimization (90C26) Nonsmooth analysis (49J52) Inverse problems for PDEs (35R30) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Inequalities involving derivatives and differential and integral operators (26D10)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Convex Tikhonov regularization in Banach spaces: new results on convergence rates
- Proximal alternating linearized minimization for nonconvex and nonsmooth problems
- Regularization methods in Banach spaces.
- Nonlinear error bounds via a change of function
- The Łojasiewicz gradient inequality in the infinite-dimensional Hilbert space framework
- Asymptotics for a class of non-linear evolution equations, with applications to geometric problems
- On the convergence of the proximal algorithm for nonsmooth functions involving analytic features
- On gradients of functions definable in o-minimal structures
- On ill-posedness and a Tikhonov regularization for a multidimensional inverse hyperbolic problem
- A converse result for Banach space convergence rates in Tikhonov-type convex regularization of ill-posed linear equations
- Existence of variational source conditions for nonlinear inverse problems in Banach spaces
- Using Landweber iteration to quantify source conditions -- a numerical study
- Splitting methods with variable metric for Kurdyka-Łojasiewicz functions and general convergence rates
- Penalty-based smoothness conditions in convex variational regularization
- Cubic regularization of Newton method and its global performance
- GLOBAL UNIQUENESS AND STABILITY IN DETERMINING COEFFICIENTS OF WAVE EQUATIONS
- METRIC REGULARITY—A SURVEY PART 1. THEORY
- Characterizations of Łojasiewicz inequalities: Subgradient flows, talweg, convexity
- One new strategy for a priori choice of regularizing parameters in Tikhonov's regularization
- Stability for an inverse boundary problem of determining a part of a boundary
- Proximal-gradient algorithms for fractional programming
- The Łojasiewicz Inequality for Nonsmooth Subanalytic Functions with Applications to Subgradient Dynamical Systems
- Characterizations of error bounds for lower semicontinuous functions on metric spaces
- Convergence of the Iterates of Descent Methods for Analytic Cost Functions
- Conditional stabilizing estimation for an integral equation of first kind with analytic kernel