Results 21 to 30 of about 11,050,393 (374)
On Hadamard inequalities for refined convex functions via strictly monotone functions
AIMS Mathematics, 2022 In this paper, we define refined (α,h−m)-convex function with respect to a strictly monotone function. This function provides refinements of various well-known classes of functions for specific strictly monotone functions.
Moquddsa Zahra +3 more
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Non-convex Optimization for Machine Learning [PDF]
Found. Trends Mach. Learn., 2017 A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low rank are ...
Prateek Jain, Purushottam Kar
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An application of the generalized Bessel function [PDF]
Mathematica Bohemica, 2017 We introduce and study some new subclasses of starlike, convex and close-to-convex functions defined by the generalized Bessel operator. Inclusion relations are established and integral operator in these subclasses is discussed.
Hanan Darwish +2 more
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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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Optimal Rates for Zero-Order Convex Optimization: The Power of Two Function Evaluations [PDF]
IEEE Transactions on Information Theory, 2013 We consider derivative-free algorithms for stochastic and nonstochastic convex optimization problems that use only function values rather than gradients.
John C. Duchi +3 more
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Uniformly starlike functions and uniformly convex functions related to the Pascal distribution [PDF]
Mathematica Bohemica, 2021 In this article, we aim to find sufficient conditions for a convolution of analytic univalent functions and the Pascal distribution series to belong to the families of uniformly starlike functions and uniformly convex functions in the open unit disk ...
Gangadharan Murugusundaramoorthy +1 more
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Conditionally approximately convex functions
Demonstratio Mathematica, 2016 Let X be a real normed space, V be a subset of X and α: [0, ∞) → [0, ∞] be a nondecreasing function. We say that a function f : V → [−∞, ∞] is conditionally α-convex if for each convex combination ∑i=0ntivi$\sum\nolimits_{i = 0}^n {t_i v_i }$ of ...
Najdecki Adam, Tabor Józef
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On φ-convexity of convex functions
Linear Algebra and its Applications, 1998 AbstractWe construct a non-trivial set φ of extended-real valued functions on Rn, containing all affine functions, such that an extended-real valued function f on Rn is convex if and only if it is φ-convex in the sense of Dolecki and Kurcyusz, i.e., the (pointwise) supremum of some subset of φ. Also, we prove a new sandwich theorem.
Ivan Singer +1 more
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On the singularities of convex functions [PDF]
Manuscripta Mathematica, 1992 Given a semi-convex functionu: ω⊂R n→R and an integerk≡[0,1,n], we show that the set ∑k defined by $$\Sigma ^k = \left\{ {x \in \Omega :dim\left( {\partial u\left( x \right)} \right) \geqslant k} \right\}$$ is countably ℋn-k i.e., it is ...
Alberti G, AMBROSIO, Luigi, Cannarsa P.
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The Ostrowski inequality for s-convex functions in the third sense
AIMS Mathematics, 2022 In this paper, the Ostrowski inequality for s-convex functions in the third sense is studied. By applying Hölder and power mean integral inequalities, the Ostrowski inequality is obtained for the functions, the absolute values of the powers of whose ...
Gültekin Tınaztepe +3 more
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