@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}
}

@article{MTMT:34729741,
	title = {Confidence level solutions for stochastic programming},
	url = {https://m2.mtmt.hu/api/publication/34729741},
	author = {Nesterov, Yurii and Vial, J.-Ph.},
	doi = {10.1016/j.automatica.2008.01.017},
	journal-iso = {AUTOMATICA},
	journal = {AUTOMATICA},
	volume = {44},
	unique-id = {34729741},
	issn = {0005-1098},
	year = {2008},
	eissn = {1873-2836},
	pages = {1559-1568}
}

@article{MTMT:1999178,
	title = {Computing multivariate normal probabilities: A new look},
	url = {https://m2.mtmt.hu/api/publication/1999178},
	author = {Gassmann, H I and Deák, István and Szántai, Tamás},
	doi = {10.1198/106186002321018876},
	journal-iso = {J COMPUT GRAPH STAT},
	journal = {JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS},
	volume = {11},
	unique-id = {1999178},
	issn = {1061-8600},
	abstract = {This article describes and compares several numerical methods for finding multivariate probabilities over a rectangle. A large computational study shows how the computation times depend on the problem dimensions, the correlation structure, the magnitude of the sought probability, and the required accuracy. No method is uniformly best for all problems and-unlike previous work-this article gives some guidelines to help establish the most promising method a priori. Numerical tests were conducted on approximately 3,000 problems generated randomly in up to 20 dimensions. Our findings indicate that direct integration methods give acceptable results for up to 12-dimensional problems, provided that the probability mass of the rectangle is not too large (less than about 0.9). For problems with small probabilities (less than 0.3) a crude Monte Carlo method gives reasonable results quickly, while bounding procedures perform best on problems with large probabilities (> 0.9). For larger problems numerical integration with quasirandom Korobov points may be considered, as may a decomposition method due to Deák. The best method found four-digit accurate probabilities for every 20-dimensional problem in less than six minutes on a 533MHz Pentium III computer.},
	keywords = {MODEL; simulation; BOUNDS; computation; multivariate normal distribution; Rectangular probability; NORMAL RECTANGLE PROBABILITIES},
	year = {2002},
	eissn = {1537-2715},
	pages = {920-949}
}

@article{MTMT:2617024,
	title = {Improved bounds and simulation procedures on the value of the multivariate normal probability distribution function},
	url = {https://m2.mtmt.hu/api/publication/2617024},
	author = {Szántai, Tamás},
	doi = {10.1023/A:1019211000153},
	journal-iso = {ANN OPER RES},
	journal = {ANNALS OF OPERATIONS RESEARCH},
	volume = {100},
	unique-id = {2617024},
	issn = {0254-5330},
	abstract = {Improved bounds and simulation procedures on the value of the
		multivariate normal probability distribution function value are given
		in the paper. The authors variance reduction technique was based on the
		Bonferroni bounds involving the first two binomial moments only. The
		new variance reduction technique is adapted to the most refined new
		bounds developed in the last decade for the estimation the probability
		of union respectively intersection of events. Numerical test results
		prove the efficiency of the simulation procedures described in the
		paper.},
	year = {2000},
	eissn = {1572-9338},
	pages = {85-101}
}

@article{MTMT:2654382,
	title = {Hipercseresznyefákkal adott valószínűségi korlátok. Probability bounds given by hypercherry trees},
	url = {https://m2.mtmt.hu/api/publication/2654382},
	author = {Bukszár, József and Szántai, Tamás},
	journal-iso = {ALK MAT LAP},
	journal = {ALKALMAZOTT MATEMATIKAI LAPOK},
	volume = {19},
	unique-id = {2654382},
	issn = {0133-3399},
	year = {1999},
	pages = {69-85}
}

@CONFERENCE{MTMT:2694566,
	title = {A computer code for solution of probabilistic constrained stochastic programming problems},
	url = {https://m2.mtmt.hu/api/publication/2694566},
	author = {Szántai, Tamás},
	booktitle = {Numerical Techniques for Stochastic Programming Problems, Springer Series in Computational Mathematics},
	unique-id = {2694566},
	year = {1988},
	pages = {229-235}
}

@article{MTMT:2002241,
	title = {Computing probabilities of rectangles in case of multinormal distribution},
	url = {https://m2.mtmt.hu/api/publication/2002241},
	author = {Deák, István},
	doi = {10.1080/00949658608810951},
	journal-iso = {J STAT COMPUT SIM},
	journal = {JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION},
	volume = {26},
	unique-id = {2002241},
	issn = {0094-9655},
	year = {1986},
	eissn = {1563-5163},
	pages = {101-114}
}

@mastersthesis{MTMT:2617134,
	title = {Többdimenziós valószínűség-eloszlásokkal kapcsolatos valószínűségek numerikus meghatározásáról},
	url = {https://m2.mtmt.hu/api/publication/2617134},
	author = {Szántai, Tamás},
	unique-id = {2617134},
	year = {1985}
}

@article{MTMT:2008597,
	title = {Three digit accurate multiple normal probabilities},
	url = {https://m2.mtmt.hu/api/publication/2008597},
	author = {Deák, István},
	doi = {10.1007/BF01399006},
	journal-iso = {NUMER MATH},
	journal = {NUMERISCHE MATHEMATIK},
	volume = {35},
	unique-id = {2008597},
	issn = {0029-599X},
	abstract = {Computer algorithms are presented for evaluating the multidimensional normal distribution function by Monte Carlo techniques. The computation of such probabilities is frequently required in stochastic programming models and in multivariate statistical problems. Using a medium size computer, three significant digits can be obtained up to ten dimensions in five seconds, up to twenty dimensions in one minute and up to fifty dimensions in ten minutes. Results of the detailed computer experiences are also reported together with some numerical examples. © 1980 Springer-Verlag.},
	keywords = {Subject Classifications: AMS (MOS): Primary 33A20, 65C05, 65D20, Secondary 49D99, CR: 5.16, 5.5},
	year = {1980},
	eissn = {0945-3245},
	pages = {369-380}
}

@article{MTMT:2617117,
	title = {Egy eljárás a többdimenziós normális eloszlásfüggvény és gradiense értékeinek meghatározására},
	url = {https://m2.mtmt.hu/api/publication/2617117},
	author = {Szántai, Tamás},
	journal-iso = {ALK MAT LAP},
	journal = {ALKALMAZOTT MATEMATIKAI LAPOK},
	volume = {2},
	unique-id = {2617117},
	issn = {0133-3399},
	year = {1976},
	pages = {27-39}
}