@article{MTMT:33337865, title = {On the Convexity of Level-Sets of Probability Functions}, url = {https://m2.mtmt.hu/api/publication/33337865}, author = {Laguel, Yassine and van Ackooij, Wim and Malick, Jerome and Ramalho, Guilherme Matiussi}, journal-iso = {J CONVEX ANAL}, journal = {JOURNAL OF CONVEX ANALYSIS}, volume = {29}, unique-id = {33337865}, issn = {0944-6532}, abstract = {In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision vector. Even if the original set of inequalities is convex, this favourable property is not immediately transferred to the probabilistically constrained feasible set and may in particular depend on the chosen safety level. In this paper, we provide results guaranteeing the convexity of feasible sets to probabilistic constraints when the safety level is greater than a computable threshold. Our results extend all the existing ones and also cover the case where decision vectors belong to Banach spaces. The key idea in our approach is to reveal the level of underlying convexity in the nominal problem data (e.g., concavity of the probability function) by auxiliary transforming functions. We provide several examples illustrating our theoretical developments.}, keywords = {Stochastic optimization; Convex analysis; Probability constraints; Elliptical distributions}, year = {2022}, eissn = {0944-6532}, pages = {411-442} } @inbook{MTMT:32601778, title = {Fogyasztás ütemezési probléma egyoldalas együttes valószínűséggel korlátozott sztochasztikus modellje. A stochastic model of the one-sided joint probability constrained consumption scheduling problem}, url = {https://m2.mtmt.hu/api/publication/32601778}, author = {Drenyovszki, Rajmund}, booktitle = {Kutatás és innováció 2021}, unique-id = {32601778}, year = {2021}, pages = {389-394} } @article{MTMT:31609283, title = {A Discussion of Probability Functions and Constraints from a Variational Perspective}, url = {https://m2.mtmt.hu/api/publication/31609283}, author = {van Ackooij, Wim}, doi = {10.1007/s11228-020-00552-2}, journal-iso = {SET-VALUED VAR ANAL}, journal = {SET-VALUED AND VARIATIONAL ANALYSIS}, volume = {28}, unique-id = {31609283}, issn = {1877-0533}, year = {2020}, eissn = {1877-0541}, pages = {585-609} } @article{MTMT:3323588, title = {Probability maximization by inner approximation}, url = {https://m2.mtmt.hu/api/publication/3323588}, author = {Fábián, Csaba and Gurka Dezsőné Csizmás, Edit Margit and Drenyovszki, Rajmund and Wim, van Ackooij and Vajnai, Tibor and Kovács, Lóránt and Szántai, Tamás}, doi = {10.12700/APH.15.1.2018.1.7}, journal-iso = {ACTA POLYTECH HUNG}, journal = {ACTA POLYTECHNICA HUNGARICA}, volume = {15}, unique-id = {3323588}, issn = {1785-8860}, abstract = {We solve probability maximization problems using an approximation scheme that is analogous to the classic approach of p-efficient points, proposed by Prékopa to handle chance constraints. But while p-efficient points yield an approximation of a level set of the probabilistic function, we approximate the epigraph. The present scheme is easy to implement and is immune to noise in gradient computation. © 2018, Budapest Tech Polytechnical Institution. All rights reserved.}, year = {2018}, eissn = {1785-8860}, pages = {105-125}, orcid-numbers = {Fábián, Csaba/0000-0002-9446-1566; Gurka Dezsőné Csizmás, Edit Margit/0000-0003-4397-1758; Drenyovszki, Rajmund/0000-0002-9462-2729} }