Uncontrolled inexact information within bundle methods
EURO Journal on Computational Optimization, 2017 We consider convex non-smooth optimization problems where additional information with uncontrolled accuracy is readily available. It is often the case when the objective function is itself the output of an optimization solver, as for large-scale energy ...
Jérôme Malick +2 more
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A relaxed version of the gradient projection method for variational inequalities with applications
, 2022 In this paper, we propose a relaxed version of the gradient projection method for strongly monotone variational inequalities defined on a level set of a (possibly non-differentiable) convex function.
THE VINH, Nguyen, THI THUONG, Ngo
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ON THE CONVEXITY OF PIECEWISE-DEFINED FUNCTIONS ∗, ∗∗, ∗∗∗ [PDF]
, 2016 . Functions that are piecewise defined are a common sight in mathematics while convexity is a property especially desired in optimization. Suppose now a piecewise-defined function is convex on each of its defining components — when can we conclude that ...
Lucet, Yves +5 more
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Cascading: an adjusted exchange method for robust conic programming
, 2006 Robust programming, Conic programming, Semi-infinite programming, Exchange method, 90C34, 90C25,
Ralf Werner, Werner, Ralf, Werner, R.
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Two Relaxed Inertial Forward–Reflected–Backward Splitting Algorithms With Momentum Terms
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this paper, to solve the monotone inclusion problem consisting of the sum of two monotone operators in Hilbert spaces, we propose and study two modifications of Malitsky–Tam’s forward–reflection–backward splitting methods with double momentum terms. Meanwhile, we consider a relaxed inertial version to expand the range of allowable step sizes.
Binbin Zhang +3 more
wiley +1 more source
Generalized derivatives and nonsmooth optimization, a finite dimensional tour
, 2005 Convex optimization, nonsmooth analysis, nonsmooth optimization, set-valued maps, variational analysis, mathematical programming, nonconvex programming, nonlinear programming, optimality conditions, second order conditions, tangent cones, normal cones ...
Joydeep Dutta
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The robust isolated calmness of spectral norm regularized convex matrix optimization problems
Open MathematicsThis article aims to provide a series of characterizations of the robust isolated calmness of the Karush-Kuhn-Tucker (KKT) mapping for spectral norm regularized convex optimization problems. By establishing the variational properties of the spectral norm
Yin Ziran, Chen Xiaoyu, Zhang Jihong
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Central axes and peripheral points in high dimensional directional datasets.
, 2015 International audienceWe introduce a new notion of central axis for a finite set {a 1 ,. .. , a m } of vectors in R n. In tandem, we discuss different ways of measuring the dispersion of the data points a i 's around the central axis. Finally, we explain
Seeger, Alberto +2 more
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Principles of Extremum and Application to some Problems of Analysis [PDF]
, 1998 AMS subject classification: 41A17, 41A50, 49Kxx, 90C25.The aim of this paper is to demonstrate applications of a direct approach to the solution of extremal problems to some concrete problems of classical analysis, calculus of variations and ...
Tikhomirov, V.
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Proximal methods for a class of bilevel monotone equilibrium problems
Bilevel problem, Variational inequality, Monotonicity, Equilibrium problem, Proximal method, 90C25, 49M45, 65C25,
Abdellatif Moudafi
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