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Convex Functions and Spacetime Geometry
, 2001 Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial data set $(\Sigma,
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Conic geometric optimisation on the manifold of positive definite matrices
, 2014 We develop \emph{geometric optimisation} on the manifold of Hermitian positive definite (HPD) matrices. In particular, we consider optimising two types of cost functions: (i) geodesically convex (g-convex); and (ii) log-nonexpansive (LN).
Hosseini, Reshad, Sra, Suvrit
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Hermite–Hadamard–Fejér type inequalities for p-convex functions
Arab Journal of Mathematical Sciences, 2017 In this paper, firstly, Hermite–Hadamard–Fejér type inequalities for p-convex functions are built. Secondly, an integral identity and some Hermite–Hadamard–Fejér type integral inequalities for p-convex functions are obtained.
Mehmet Kunt, İmdat İşcan
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Handling convexity-like constraints in variational problems
, 2014 We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies.
Mérigot, Quentin, Oudet, Edouard
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Inequalities of Jensen type for \(AH\)-convex functions
Journal of Numerical Analysis and Approximation Theory, 2016 Some integral inequalities of Jensen type for AH-convex functions defined on intervals of real line are given. Applications for power and logarithm functions are provided as well.
Sever Dragomir
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On the Sublinear Convergence Rate of Multi-Block ADMM
, 2015 The alternating direction method of multipliers (ADMM) is widely used in solving structured convex optimization problems. Despite of its success in practice, the convergence properties of the standard ADMM for minimizing the sum of $N$ $(N\geq 3)$ convex
Lin, Tianyi +2 more
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New inequalities of Hermite-Hadamard type for HA-convex functions
Journal of Numerical Analysis and Approximation Theory, 2018 Some new inequalities of Hermite-Hadamard type for HA-convex functions defined on positive intervals are given.
Sever Dragomir
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Inequalities of Jensen type for h-convex functions on linear spaces [PDF]
Mathematica Moravica, 2015 Some inequalities of Jensen type for h-convex functions defined on convex subsets in real or complex linear spaces are given. Applications for norm inequalities are provided as well.
Sever Silvestru Dragomir
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Hermite-Hadamard type inequalities for p-convex functions via fractional integrals
Moroccan Journal of Pure and Applied Analysis, 2017 In this paper, we present Hermite-Hadamard inequality for p-convex functions in fractional integral forms. we obtain an integral equality and some Hermite-Hadamard type integral inequalities for p-convex functions in fractional integral forms.
Kunt Mehmet, İşcan İmdat
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Hermite-Hadamard type inequalities for Wright-convex functions of several variables
, 2014 We present Hermite--Hadamard type inequalities for Wright-convex, strongly convex and strongly Wright-convex functions of several variables defined on ...
Wasowicz, Sz., Śliwińska, D.
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