Results 1 to 10 of about 10,963,226 (321)
Convex Functions on Convex Polytopes [PDF]
Proceedings of the American Mathematical Society, 1968 The behavior of convex functions is of interest in connection with a wide variety of optimization problems. It is shown here that this behavior is especially simple, in certain respects, when the domain is a polytope or belongs to certain classes of sets closely related to polytopes; moreover, the polytopes and related classes are actually ...
David Gale +2 more
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Modulus of convexity for operator convex functions [PDF]
Journal of Mathematical Physics, 2014 Given an operator convex function $f(x)$, we obtain an operator-valued lower bound for $cf(x) + (1-c)f(y) - f(cx + (1-c)y)$, $c \in [0,1]$. The lower bound is expressed in terms of the matrix Bregman divergence.
Kim, Isaac H.
core +8 more sources
Valuations on Convex Functions [PDF]
International Mathematics Research Notices, 2017 All continuous, SL$(n)$ and translation invariant valuations on the space of convex functions on ${\mathbb R}^n$ are completely classified.
A. Colesanti, M. Ludwig, F. Mussnig
semanticscholar +6 more sources
On an Inequality for Convex Functions [PDF]
Proceedings of the American Mathematical Society, 1956 H. D. Brunk
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Functions with convex means [PDF]
Pacific Journal of Mathematics, 1964 T. K. Boehme, A. M. Bruckner
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Convex Optimization, 2021 This paper will analyze convex functions. In particular, it will investigate criteria for convexity. The investigation will list the criteria from the weakest to the strongest based on theorems, definitions, propositions, and various examples. The theory
Susanna Maria Zagar
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The Hadwiger Theorem on Convex Functions, I [PDF]
Geometric and Functional Analysis, 2020 A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on ${\mathbb{R}}^{n}$ is established.
A. Colesanti, M. Ludwig, F. Mussnig
semanticscholar +1 more source
Stochastic model-based minimization of weakly convex functions [PDF]
SIAM Journal on Optimization, 2018 We consider an algorithm that successively samples and minimizes stochastic models of the objective function. We show that under weak-convexity and Lipschitz conditions, the algorithm drives the expected norm of the gradient of the Moreau envelope to ...
Damek Davis, D. Drusvyatskiy
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Some new Simpson's type inequalities for coordinated convex functions in quantum calculus
Mathematical methods in the applied sciences, 2020 In this article, by using the notion of newly defined q1q2 derivatives and integrals, some new Simpson's type inequalities for coordinated convex functions are proved. The outcomes raised in this paper are extensions and generalizations of the comparable
M. Ali +3 more
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