TY  - JOUR
AU  - Laguel, Yassine
AU  - van Ackooij, Wim
AU  - Malick, Jerome
AU  - Ramalho, Guilherme Matiussi
TI  - On the Convexity of Level-Sets of Probability Functions
JF  - JOURNAL OF CONVEX ANALYSIS
J2  - J CONVEX ANAL
VL  - 29
PY  - 2022
IS  - 2
SP  - 411
EP  - 442
PG  - 32
SN  - 0944-6532
UR  - https://m2.mtmt.hu/api/publication/33337865
ID  - 33337865
AB  - 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.
LA  - English
DB  - MTMT
ER  - 

TY  - CHAP
AU  - Drenyovszki, Rajmund
ED  - Johanyák, Zsolt Csaba
ED  - Kovács, Lóránt
ED  - Pásztor, Attila
ED  - Ferenczy, Tibor
ED  - Weltsch, Zoltán
ED  - Tóth, Ákos
ED  - Dobjánné Antal, Elvira
TI  - Fogyasztás ütemezési probléma egyoldalas együttes valószínűséggel korlátozott sztochasztikus modellje. A stochastic model of the one-sided joint probability constrained consumption scheduling problem
TS  - A stochastic model of the one-sided joint probability constrained consumption scheduling problem
T2  - Kutatás és innováció 2021
PB  - Neumann János Egyetem GAMF Műszaki és Informatikai Kar
CY  - Kecskemét
SN  - 9786155817977
PY  - 2021
SP  - 389
EP  - 394
PG  - 6
UR  - https://m2.mtmt.hu/api/publication/32601778
ID  - 32601778
LA  - Hungarian
DB  - MTMT
ER  - 

TY  - JOUR
AU  - van Ackooij, Wim
TI  - A Discussion of Probability Functions and Constraints from a Variational Perspective
JF  - SET-VALUED AND VARIATIONAL ANALYSIS
J2  - SET-VALUED VAR ANAL
VL  - 28
PY  - 2020
IS  - 4
SP  - 585
EP  - 609
PG  - 25
SN  - 1877-0533
DO  - 10.1007/s11228-020-00552-2
UR  - https://m2.mtmt.hu/api/publication/31609283
ID  - 31609283
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Fábián, Csaba
AU  - Gurka Dezsőné Csizmás, Edit Margit
AU  - Drenyovszki, Rajmund
AU  - Wim, van Ackooij
AU  - Vajnai, Tibor
AU  - Kovács, Lóránt
AU  - Szántai, Tamás
TI  - Probability maximization by inner approximation
JF  - ACTA POLYTECHNICA HUNGARICA
J2  - ACTA POLYTECH HUNG
VL  - 15
ET  - 0
PY  - 2018
IS  - 1
SP  - 105
EP  - 125
PG  - 21
SN  - 1785-8860
DO  - 10.12700/APH.15.1.2018.1.7
UR  - https://m2.mtmt.hu/api/publication/3323588
ID  - 3323588
AB  - 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.
LA  - English
DB  - MTMT
ER  -