Results 21 to 30 of about 11,287,559 (375)
A New Advanced Class of Convex Functions with Related Results
Axioms, 2023 It is the purpose of this paper to propose a novel class of convex functions associated with strong η-convexity. A relationship between the newly defined function and an earlier generalized class of convex functions is hereby established.
Muhammad Adil Khan +3 more
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Schur-Convexity of Averages of Convex Functions [PDF]
Journal of Inequalities and Applications, 2011 The object is to give an overview of the study of Schur-convexity of various means and functions and to contribute to the subject with some new results. First, Schur-convexity of the generalized integral and weighted integral quasi-arithmetic mean is studied.
Franjić Iva +3 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
semanticscholar +1 more source
Root Function and Convex Function
Communications Faculty Of Science University of Ankara, 1974 Many authors [1], [2], [3], [4] considered the problems under different weak conditions which imply the continuity of the functions. In this section, we will consider convex functions on a commutative topological group with a root function.
Bilgezadeh, A., Pellong, C.
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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
semanticscholar +1 more source
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
doaj +1 more source
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
semanticscholar +1 more source
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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An Improved Convergence Analysis for Decentralized Online Stochastic Non-Convex Optimization [PDF]
IEEE Transactions on Signal Processing, 2020 In this paper, we study decentralized online stochastic non-convex optimization over a network of nodes. Integrating a technique called gradient tracking in decentralized stochastic gradient descent, we show that the resulting algorithm, GT-DSGD, enjoys ...
Ran Xin, U. Khan, S. Kar
semanticscholar +1 more source
DC Proximal Newton for Non-Convex Optimization Problems [PDF]
, 2015 We introduce a novel algorithm for solving learning problems where both the loss function and the regularizer are non-convex but belong to the class of difference of convex (DC) functions.
Flamary, Remi +2 more
core +4 more sources