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Mathematics of Operations Research, 1998
We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set U, yet the constraints must hold for all possible values of the data from U.
A. Ben-Tal, A. Nemirovski
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We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set U, yet the constraints must hold for all possible values of the data from U.
A. Ben-Tal, A. Nemirovski
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Convex Bodies: The Brunn–Minkowski Theory: Minkowski addition
, 19931. Basic convexity 2. Boundary structure 3. Minkowski addition 4. Curvature measure and quermass integrals 5. Mixed volumes 6. Inequalities for mixed volumes 7. Selected applications Appendix.
R. Schneider
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Cell Detection with Star-convex Polygons
International Conference on Medical Image Computing and Computer-Assisted Intervention, 2018Automatic detection and segmentation of cells and nuclei in microscopy images is important for many biological applications. Recent successful learning-based approaches include per-pixel cell segmentation with subsequent pixel grouping, or localization ...
Uwe Schmidt +3 more
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Online Learning and Online Convex Optimization
Found. Trends Mach. Learn., 2012Online learning is a well established learning paradigm which has both theoretical and practical appeals. The goal of online learning is to make a sequence of accurate predictions given knowledge of the correct answer to previous prediction tasks and ...
Shai Shalev-Shwartz
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Convexity and convex sets [PDF]
, 2010 The history of convexity History of convexity is rather astonishing, even paradoxical, and we explain why. On the one hand, the notion of convexity Convexity is extremely natural, so much so that we find it, for example, in works on artArt and anatomyAnatomy without it being defined.
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Lower bounds for non-convex stochastic optimization
Mathematical programming, 2019We lower bound the complexity of finding $$\epsilon $$ ϵ -stationary points (with gradient norm at most $$\epsilon $$ ϵ ) using stochastic first-order methods.
Yossi Arjevani +5 more
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Convex analysis in general vector spaces
, 2002Preliminary Results on Functional Analysis Convex Analysis in Locally Convex Spaces Some Results and Applications of Convex Analysis in Normed Spaces.
C. Zălinescu
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Convexity without convex combinations
Journal of Geometry, 2015Separation theorems play a central role in the theory of Functional Inequalities. The importance of Convex Geometry has led to the study of convexity structures induced by Beckenbach families. The aim of the present note is to replace recent investigations into the context of an axiomatic setting, for which Beckenbach structures serve as models ...
Mihály Bessenyei, Bella Popovics
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Convex Functionals on Convex Sets and Convex Analysis
1985Over the last 20 years, parallel to the theory of monotone operators, a calculus for the investigation of convex functionals designated by convex analysis has emerged, which allows one to solve a number of problems in a simple way. To this calculus belong: (α) The subgradient ∂F (a generalization of the classical concept of derivative).
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