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Linear Convergence of the Derivative-Free Proximal Bundle Method on Convex Nonsmooth Functions, with Application to the Derivative-Free \(\mathcal{VU}\)-Algorithm
Proximal bundle methods are a class of optimisation algorithms that leverage the proximal operator to address nonsmoothness in the objective function...
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Conservative and Semismooth Derivatives are Equivalent for Semialgebraic Maps
Subgradient and Newton algorithms for nonsmooth optimization require generalized derivatives to satisfy subtle approximation properties:...
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Superdifferential Analysis of the Takagi-Van Der Waerden Functions
In this work we completely describe the superdifferential of the Takagi-Van der Waerden functions and, as a consequence, the local maxima of these...
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Stability of Minimization Problems and the Error Bound Condition
It is well known that Error Bound conditions provide some (usually linear or sublinear) rate of convergence for gradient descent methods in...
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Conservative Parametric Optimality and the Ridge Method for Tame Min-Max Problems
We study the ridge method for min-max problems, and investigate its convergence without any convexity, differentiability or qualification assumption....
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Sensitivity Analysis of Stochastic Constraint and Variational Systems via Generalized Differentiation
This paper conducts sensitivity analysis of random constraint and variational systems related to stochastic optimization and variational...
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Generalized Sequential Differential Calculus for Expected-Integral Functionals
Motivated by applications to stochastic programming, we introduce and study the expected-integral functionals, which are map**s given in an...
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A Discussion on Variational Analysis in Derivative-Free Optimization
Variational Analysis studies mathematical objects under small variations. With regards to optimization, these objects are typified by representations...
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On the Positive Definiteness of Limiting Coderivative for Set-Valued Map**s
This paper concerns the interconnection between the positive definiteness of limiting coderivative and the local strong maximal monotonicity of...
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Risk-Averse Stochastic Programming and Distributionally Robust Optimization Via Operator Splitting
This work deals with a broad class of convex optimization problems under uncertainty. The approach is to pose the original problem as one of finding...
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On the Quantitative Solution Stability of Parameterized Set-Valued Inclusions
The subject of the present paper are stability properties of the solution set to set-valued inclusions. The latter are problems emerging in robust...
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Sufficient Conditions for Metric Subregularity of Constraint Systems with Applications to Disjunctive and Ortho-Disjunctive Programs
This paper is devoted to the study of the metric subregularity constraint qualification for general optimization problems, with the emphasis on the...
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Transversality Properties: Primal Sufficient Conditions
The paper studies ‘good arrangements’ (transversality properties) of collections of sets in a normed vector space near a given point in their...
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Bornological Coderivative and Subdifferential Calculus in Smooth Banach Spaces
In this paper, we study bornological generalized differential properties of sets with nonsmooth boundaries, nonsmooth functions, and set-valued...
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Linearized M-stationarity Conditions for General Optimization Problems
This paper investigates new first-order optimality conditions for general optimization problems. These optimality conditions are stronger than the...
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Non-Smooth Optimization for Robust Control of Infinite-Dimensional Systems
We use a non-smooth trust-region method for H ∞ -control of infinite-dimensional systems. Our method applies in particular to distributed and boundary...
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Full Stability of General Parametric Variational Systems
The paper introduces and studies the notions of Lipschitzian and Hölderian full stability of solutions to three-parametric variational systems...
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Subgradient Projectors: Extensions, Theory, and Characterizations
Subgradient projectors play an important role in optimization and for solving convex feasibility problems. For every locally Lipschitz function, we...
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Epi-convergence Properties of Smoothing by Infimal Convolution
This paper concerns smoothing by infimal convolution for two large classes of functions: convex, proper and lower semicontinous as well as for (the...