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Conditioning convex and nonconvex problems

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Geometric Measure Theory

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About well-posed optimization problems for functionals in metric spaces

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Generalized arcwise-connected functions and characterizations of local-global minimum properties

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Preservation of persistence and stability under intersections and operations, part 1: Persistence

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Lipschitz behaviour of the Legendre-Fenchel Transform

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Miscellaneous incidences of convergence theories in optimization and nonlinear analysis I: Behavior of solutions

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Holder continuity of solutions to a parametric variational inequality

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On functions whose local minima are global

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Metrically well-set minimization problems

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Inversion of real-valued functions and applications

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The topology of theρ-hausdorff distance

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Well-Posed Optimization Problems

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Multifunctions and Integrands

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Convergence of convex sets and of solutions of variational inequalities

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On uniformly convex functions

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Metric regularity, openness and Lipschitzian behavior of multifunctions

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Topologies and convergences on the space of convex functions

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Geometric Measure Theory

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Operations on convergent families of sets and functions

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Topological stability results about approximate solutions of parametrized minimization problems

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Conjugate Convex Functions and the Epi-Distance Topology

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The Cosmic Hausdorff Topology, the Bounded Hausdorff Topology and Continuity of Polarity

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Isometries for the Legendre-Fenchel Transform

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Quantitative stability of variational systems. I. The epigraphical distance

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Transactions of the American Mathematical Society

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Quantitative Stability of Variational Systems II. A Framework for Nonlinear Conditioning

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Optimization and Nonsmooth Analysis

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Uniformly convex functions

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A generalized derivative for calm and stable functions

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Uniformly convex and uniformly smooth convex functions

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Proximal Mappings

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Bounded (Hausdorff) Convergence: Basic Facts and Applications

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Metric and Topological Tools

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Elements of Differential Calculus

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Elements of Convex Analysis

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Elementary and Viscosity Subdifferentials

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Circa-Subdifferentials, Clarke Subdifferentials

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Graded Subdifferentials, Ioffe Subdifferentials

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Some Links Between Approximation, Nonsmooth Analysis, Penalization and Regularization

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A Projection-Proximal Bundle Method for Convex Nondifferentiable Minimization

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Convergence and efficiency of subgradient methods for quasiconvex minimization

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Convergence of the forward-backward algorithm: beyond the worst-case with the help of geometry

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Desingularizing Functions in Convex Programming and Convergence of an Abstract Gradient Descent Algorithm

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A comparative study of various notions of approximation of sets

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A generalized Ekeland vector variational principle and its applications in optimization

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Well-Posedness and Optimization under Perturbations

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Genericity of Well-Posedness, Perturbations and Smooth Variational Principles

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Levels Sets Infimal Convolution and Level Addition

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Conditioning and Upper-Lipschitz Inverse Subdifferentials in Nonsmooth Optimization Problems

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Continuity of Usual Operations and Variational Convergences

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What is quasiconvex analysis?

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Bounded convergence for perturbed minimization problems

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Weak sharp efficiency and growth condition for vector-valued functions with applications

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Calmness and Stability Properties of Marginal and Performance Functions

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On Marginal Subgradients of Convex Functions

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Conditioning Convex and Nonconvex Functions in Optimization

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A Julia Module for Polynomial Optimization with Complex Variables applied to Optimal Power Flow

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Error Bounds and Multipliers in Constrained Optimization Problems with Tolerance

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Constrained Consensus-Based Optimization

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Degrees of Efficiency and Degrees of Minimality

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On First- and Second-Order Conditions for Error Bounds

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On Minimizing and Critical Sequences in Nonsmooth Optimization

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A Nonlinear Extension of Hoffman's Error Bounds for Linear Inequalities

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Inertial Gradient-Descent algorithms for convex minimization

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