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Closed convex function
In mathematics, a function is said to be closed if for each , the sublevel set is a closed set. Equivalently, if the epigraph defined by is closed…
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Related topics
Related topics
5 relations
Broader (1)
Convex analysis
Convex conjugate
Convex function
Epigraph (mathematics)
Proper convex function
Papers overview
Semantic Scholar uses AI to extract papers important to this topic.
2019
2019
Accelerated Regularized Newton Methods for Minimizing Composite Convex Functions
G. N. Grapiglia
,
Y. Nesterov
SIAM J. Optim.
2019
Corpus ID: 117728691
In this paper, we study accelerated Regularized Newton Methods for minimizing objectives formed as a sum of two functions: one is…
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2019
2019
A block symmetric Gauss–Seidel decomposition theorem for convex composite quadratic programming and its applications
Xudong Li
,
Defeng Sun
,
K. Toh
Math. Program.
2019
Corpus ID: 724294
For a symmetric positive semidefinite linear system of equations $$\mathcal{Q}{{\varvec{x}}}= {{\varvec{b}}}$$Qx=b, where…
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Highly Cited
2018
Highly Cited
2018
A proximal difference-of-convex algorithm with extrapolation
Bo Wen
,
Xiaojun Chen
,
Ting Kei Pong
Comput. Optim. Appl.
2018
Corpus ID: 4339491
We consider a class of difference-of-convex (DC) optimization problems whose objective is level-bounded and is the sum of a…
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Highly Cited
2016
Highly Cited
2016
Computationally Tractable Counterparts of Distributionally Robust Constraints on Risk Measures
Krzysztof Postek
,
D. D. Hertog
,
B. Melenberg
SIAM Rev.
2016
Corpus ID: 2609542
In this paper we study distributionally robust constraints on risk measures (such as standard deviation less the mean…
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Highly Cited
2015
Highly Cited
2015
Accelerated Mirror Descent in Continuous and Discrete Time
Walid Krichene
,
A. Bayen
,
P. Bartlett
NIPS
2015
Corpus ID: 6661061
We study accelerated mirror descent dynamics in continuous and discrete time. Combining the original continuous-time motivation…
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Review
2009
Review
2009
What Shape Is Your Conjugate? A Survey of Computational Convex Analysis and Its Applications
Y. Lucet
SIAM J. Optim.
2009
Corpus ID: 1676762
Computational convex analysis algorithms have been rediscovered several times in the past by researchers from different fields…
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Review
2005
Review
2005
Convex risk measures for portfolio optimization and concepts of flexibility
H. Lüthi
,
J. Doege
Math. Program.
2005
Corpus ID: 2473075
Due to their axiomatic foundation and their favorable computational properties convex risk measures are becoming a powerful tool…
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2005
2005
Convergence of a Hybrid Projection-Proximal Point Algorithm Coupled with Approximation Methods in Convex Optimization
F. Alvarez
,
Miguel Carrasco
,
K. Pichard
Math. Oper. Res.
2005
Corpus ID: 11568399
In order to minimize a closed convex function that is approximated by a sequence of better behaved functions, we investigate the…
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1996
1996
An asymptotical variational principle associated with the steepest descent method for a convex function.
B. Lemaire
1996
Corpus ID: 16677062
Let X be a real Hilbert space endowed with inner product 〈., .〉 and associated norm ‖.‖, and let f be a proper closed convex…
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Highly Cited
1974
Highly Cited
1974
Conjugate Duality and Optimization
R. Tyrrell Rockafellar
1974
Corpus ID: 9072945
Kuhn-Tucker condition (0, 0) e dK(x, y) into a more explicit and familiar form. Writing where -k(y) = /0(x) + ylfl(x…
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