Results 11 to 20 of about 11,086,842 (321)
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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Convex Defining Functions for Convex Domains [PDF]
Journal of Geometric Analysis, 2010 21 ...
Jeffery D. McNeal, A. K. Herbig
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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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On φ-convexity of convex functions
Linear Algebra and its Applications, 1998 The authors construct a non-trivial set \(\Phi\) of extended-real valued functions on \(R^n\) containing all affine functions, such that an extended-real valued function defined on \(R^n\) is convex if and only if it is \(\Phi\)-convex, i.e., it is the pointwise supremum of some subset of \(\Phi\). They also prove a new sandwich theorem.
Ivan Singer +1 more
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Projections Onto Convex Sets (POCS) Based Optimization by Lifting [PDF]
, 2013 Two new optimization techniques based on projections onto convex space (POCS) framework for solving convex and some non-convex optimization problems are presented.
Bozkurt, A. +7 more
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Association of Jensen’s inequality for s-convex function with Csiszár divergence
Journal of Inequalities and Applications, 2019 In the article, we establish an inequality for Csiszár divergence associated with s-convex functions, present several inequalities for Kullback–Leibler, Renyi, Hellinger, Chi-square, Jeffery’s, and variational distance divergences by using particular s ...
M. Adil Khan +4 more
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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
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Quotients of continuous convex functions on nonreflexive Banach spaces [PDF]
, 2007 On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and
Holicky, P. +3 more
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Approximately convex functions [PDF]
Proceedings of the American Mathematical Society, 1952 So far we have discussed the stability of various functional equations. In the present section, we consider the stability of a well-known functional inequality, namely the inequality defining convex functions: $$f\left( {\lambda x + \left( {1 - \lambda } \right)y} \right) \leqslant \lambda f\left( x \right) + \left( {1 - \lambda } \right)f\left( y \
Stanislaw M. Ulam, Donald H. Hyers
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