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, 2015
The BMV conjecture states that for $$n\times n$$n×n Hermitian matrices $$A$$A and $$B$$B the function $$f_{A,B}(t)={{\mathrm{trace\,}}}e^{tA+B}$$fA,B(t)=traceetA+B is exponentially convex. Recently the BMV conjecture was proved by Herbert Stahl.
V. Katsnelson
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The BMV conjecture states that for $$n\times n$$n×n Hermitian matrices $$A$$A and $$B$$B the function $$f_{A,B}(t)={{\mathrm{trace\,}}}e^{tA+B}$$fA,B(t)=traceetA+B is exponentially convex. Recently the BMV conjecture was proved by Herbert Stahl.
V. Katsnelson
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Properties of Exponentially m-Convex Functions
2020In this paper, we define and introduce some new concepts of the exponentially m-convex functions involving a fixed constant m ∈ (0, 1]. We investigate several properties of the exponentially m-convex functions and discuss their relations with convex functions. Optimality conditions are characterized by a class of variational inequalities.
Muhammad Aslam Noor, Khalida Inayat Noor
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Relative Strongly Exponentially Convex Functions
2020In this paper, we define and consider some new concepts of the strongly exponentially convex functions involving an arbitrary negative bifunction. Some properties of these strongly exponentially convex functions are investigated under suitable conditions.
Muhammad Aslam Noor +2 more
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Computational and Applied Mathematics, 2023
Xavier Emery, Emilio Porcu
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Xavier Emery, Emilio Porcu
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Exponentially fast distributed coordination for nonsmooth convex optimization
2016 IEEE 55th Conference on Decision and Control (CDC), 2016This paper considers networks of agents that seek to cooperatively solve a general class of nonsmooth convex optimization problems with an inherent distributed structure. We characterize the asymptotic convergence properties of distributed continuous-time coordination algorithms whose design relies on the saddle-point dynamics associated with an ...
Simon K. Niederländer +2 more
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The exponentiated convex variable step-size (ECVSS) algorithm
Signal Processing, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Corneliu Rusu, Colin F. N. Cowan
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Harmonic Exponential Convex Functions and Inequalities
2019In this chapter, we intend to introduce and study a new class of harmonic exponential h-convex functions. We show that this class includes several new and previously known classes of harmonic convex functions. We derive several Hermite–Hadamard type integral inequalities. Numerous special cases are also discussed.
Muhammad Uzair Awan +2 more
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Generalized Kernels of the Toeplitz Type for Exponentially Convex Functions
Ukrainian Mathematical Journal, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Distributions of Exponential Growth with Support in a Proper Convex Cone
Publications of the Research Institute for Mathematical Sciences, 2004In this paper we will characterize the spaces of distributions of exponential growth with support in a proper convex cone by the heat kernel method. As application we can obtain the Paley–Wiener theorem for distributions of exponential growth supported by a proper convex cone and Edge-of-the-Wedge theorem for the space of the image by the Fourier ...
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