Sándor Zoltán Németh

arXiv2022

Convexity of sets and quadratic functions on the hyperbolic space

In this paper some concepts of convex analysis on hyperbolic space are studied. We first study properties of the intrinsic distance, for instance, we present the spectral decomposition of its Hessian. Next, we study the concept of convex sets and the intrinsic projection onto these sets. We also study the concept of convex functions and present first and second order characterizations of these functions, as well as some optimization concepts related to them. An extensive study of the hyperbolically convex quadratic functions is also presented.

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arXiv2019

Stochastic Linear Complementarity Problems on Extended Second Order Cones

In this paper, we study the stochastic linear complementarity problems on extended second order cones (stochastic ESOCLCP). We first convert the problem to a stochastic mixed complementarity problem on the nonegative orthant (SMixCP). Enlightened by the idea of Chen and Lin(2011), we introduce the Conditional Value-at-risk (CVaR) method to measure the loss of complementarity in the stochastic case. A CVaR - based minimisation problem is introduced to achieve a solution which is "good enough" for the complementarity requirement of the original SMixCP. Smoothing function and sample average approximation methods are introduced and the the problem is converted to a form which can be solved by Levenberg-Marquardt smoothing SAA algorithm. At the end of the paper a numerical example illustrates our results.

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