Results 61 to 70 of about 51,346 (174)
Private Convex Optimization via Exponential Mechanism
Journal of Privacy and ConfidentialityIn this paper, we study private optimization problems for non-smooth convex functions $F(x)=\mathbb{E}_i f_i(x)$ on $\mathbb{R}^d$.We show that modifying the exponential mechanism by adding an $\ell_2^2$ regularizer to $F(x)$ and sampling from $\pi(x)\propto \exp(-k(F(x)+\mu\|x\|_2^2/2))$ recovers both the known optimal empirical risk and population ...
Sivakanth Gopi, Yin Tat Lee, Daogao Liu
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Exponential convexity and Jensen's inequality for divided differences
Journal of Mathematical Inequalities, 2011 In this paper we obtain means which involve divided differences for n-convex functions. We examine their monotonicity property using exponentially convex functions.
Pečarić, Josip +2 more
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Moment inequalities for functions of independent random variables
, 2005 A general method for obtaining moment inequalities for functions of independent random variables is presented. It is a generalization of the entropy method which has been used to derive concentration inequalities for such functions [Boucheron, Lugosi and
Boucheron, Stephane +3 more
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Hermite–Hadamard type inequalities for exponentially p-convex functions and exponentially s-convex functions in the second sense with applications [PDF]
Journal of Inequalities and Applications, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Naila Mehreen, Matloob Anwar
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Approximations and inequalities for the exponential beta function
Journal of Inequalities and Applications, 2019 In this paper, motivated by interest in simulating the expenditure patterns of construction projects, we introduce the mathematical concept of Exponential-Beta function by F(α,β):=∫01exp[xα(1−x)β]dx, $$ F ( \alpha ,\beta ) := \int _{0}^{1}\exp \bigl[ x^{\
Silvestru Sever Dragomir +1 more
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Heliyon, 2020 In this paper, the idea and its algebraic properties of n–polynomial exponential type p–convex function have been investigated. Authors prove new trapezium type inequality for this new class of functions.
Saad Ihsan Butt +5 more
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Exponential Family Matrix Completion under Structural Constraints [PDF]
, 2015 We consider the matrix completion problem of recovering a structured matrix from noisy and partial measurements. Recent works have proposed tractable estimators with strong statistical guarantees for the case where the underlying matrix is low--rank, and
Ghosh, Joydeep +2 more
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Exponentially $ E $-convex vector optimization problems
Journal of Industrial and Management OptimizationzbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the refinements of Jensen Mercer's inequality
Journal of Numerical Analysis and Approximation Theory, 2012 In this paper we give refinements of Jensen-Mercer's inequality and its generalizations and give applications for means. We prove \(n\)-exponential convexity of the functions constructed from these refinements. At the end we discuss some examples.
M. Adil Khan, Asif R. Khan, J. Pečarić
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Advances in Difference Equations, 2020 In this paper, we give and study the concept of n-polynomial ( s , m ) $(s,m)$ -exponential-type convex functions and some of their algebraic properties. We prove new generalization of Hermite–Hadamard-type inequality for the n-polynomial ( s , m ) $(s,m)
Saad Ihsan Butt +5 more
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