Istvan Deak | Corvinus University of Budapest (original) (raw)

Papers by Istvan Deak

Parallel Computing, 1990

Almost all simulational computations require uniformly distributed random numbers. Generators of ... more Almost all simulational computations require uniformly distributed random numbers. Generators of uniform random numbers are considered and assessed with respect to their possible use on parallel computers. Two recent, commercially available computers are given special attention: the Connection Machine and the T Series. Feedback shift register type generators with a large Mersenne prime are recommended for implementation on these computers.

ACM Transactions on Mathematical Software, 1986

Lecture Notes in Economics and Mathematical Systems, 1998

Several simple regression estimators can be constructed to approximate the distribution function ... more Several simple regression estimators can be constructed to approximate the distribution function of the m-dimensional normal distribution along a line. These functions can be used to find the border points of the feasible region of probability constrained stochastic programming models. Computer experiences show a fast and robust behaviour of the root finding techniques.

Http Dx Doi Org 10 1080 07408170304362, Oct 29, 2010

Journal of Statistical Computation and Simulation, 1986

ABSTRACT A nemkonvex feladatok megoldására három területen is lényeges haladást értünk el: a való... more ABSTRACT A nemkonvex feladatok megoldására három területen is lényeges haladást értünk el: a valószínűségek kiszámítása, általános sztochasztikus feladatok optimalizálásában és a diszkrét sztochasztikus programozási feladatok megoldásában. A normális valószínűségek kiszámítására használt számítógépes szubrutinok olyan gyors működését értük el, hogy normális eloszlás esetén még 1000 dimenziós egyszerű konvex alakzatok valószínűségét is meg lehet határozni egy másodperc körüli időben. A poliéderek használatán alapuló módszer egy új elvi alapokat felhasználó eljárás valószínűségek kiszámítására. Ezen kívül a Dirichlet és a gamma eloszlás valószínűségeinek kiszámításában sikerült eredményeket elérni. Sztochasztikus feladatok megoldó algoritmusaira négy új eljárást dolgoztunk ki: a megengedett megoldások halmazának közelitésén (Bukszár), a szukcesszív regressziós approximációk véletlen egyenletrendszerekre való alkalmazása (Deák), metszősík algoritmusokat használó algoritmus (Fábián), a valószínűségi korláton belül tetszőleges helyen véletlent tartalmazó modell megoldása (Vizvári). A többdimenziós momentumproblémák megoldására kifejlesztett eljárásokat hasznossági függvény becslésére alkalmaztuk. | In our research for solving nonconvex problems we achieved progress in three areas: computing probabilities, optimizing general stochastic programming problems and discrete programming problems. The computer subroutines determining multinormal probabilities became so fast, that even for 1000 dimensional simple convex sets we were able to compute probabilities in about 1 sec. Employing polyhedra is a theoretically new path in computing probabilities. Also we developed some algorithms for computing probabilities for the Dirichlet and the gamma distribution. Four new procedures have been developed fo optimizing stochastic programming models: approximating the set of feasible solutions (Bukszár), applying the successive regression approximations for solving random linear systems of equations (Deák), cutting plane techniques (Fábián), solving problems where the random variables may be in any place inside the probabilistic constraint (Vizvari. In the multidimensional discrete moment problems we proved some theorems, and using these results new algorithm could be presented for approximating the expected utility function.

Annals or, 2006

... where the linear optimization problem is the so-called second stage problem. The expected rec... more ... where the linear optimization problem is the so-called second stage problem. The expected recourse function can be given as Q(x) = E(Q(x,ξ)) = ∫ Q(x,ξ)d(ξ), (1) I. Deák Corvinus University of Budapest e-mail: istvan.deak@uni-corvinus.hu Springer Page 2. 80 ...

J Comput Graph Stat, 2002

ABSTRACT This article describes and compares several numerical methods for finding multivariate p... more 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.

International Journal of Computer Mathematics, 1999

RefDoc Bienvenue - Welcome. Refdoc est un service / is powered by. ...

Lecture Notes in Economics and Mathematical Systems, 2004

Recently a heuristic procedure has been developed for solving twostage stochastic programming pro... more Recently a heuristic procedure has been developed for solving twostage stochastic programming problems. Using the same ideas solution algorithms are presented here for solving probabilistic constrained problems and a model family, combining probabilistic constraint and recourse, proposed by Pnlkopa. The common feature of these algorithms is that all rely on replacing the "hard" part of the problem by an easy-to-compute regression function. Numerical examples and test results are also given.

Applied Optimization, 2001

In a recent paper the successive regression approximations method was proposed for solving equati... more In a recent paper the successive regression approximations method was proposed for solving equations for one-dimensional nonlinear functions with deterministic function values. Here we apply this method to noisy function values. A set of Fortran subroutines, performing the actual computations has been developed, among them a subroutine, capable· of computing the gradient of the multidimensional normal distribution. A short description of the method, its convergence, the subroutines and computer experiences are given in this paper. Numerical examples and results of computer runs are presented up to fifteen dimensions. According to the numerical results the error of the approximate root depends inversely on the square root of the number of points used in the approximation. 65 F. Giannessi et al. (eds.), Optimization Theory, 65-80.

Springer Series in Operations Research and Financial Engineering, 2014