List of notations Preface to the second edition Preface to the first edition 1. Stochastic programming models 2. Two-stage problems 3. Multistage problems 4. Optimization models with probabilistic constraints 5. Statistical inference 6. Risk averse optimization 7. Background material 8. Bibliographical remarks Bibliography Index.

Lectures on Stochastic Programming: Modeling and Theory

Partial Safety Factor Method Probabilistic Information Simple Reliability Index Geometric Reliability Index Generalized Reliability Index Transformation Sensitivity Analysis Monte Carlo Methods Load Combinations Statistical and Model Uncertainty Decision Philosophy Reliability of Existing Structures System Reliability Analysis Introduction to Process Descriptions.

https://chodor-projekt.net/wp-content/uploads/BiNSK/Literatura/Dilevsen,Madsen,%20Structural%20Reliability%20Methods%20(2007).pdf

Structural Reliability Methods

This paper proposes a simple modification of a conventional method of moments estimator for a discrete response model, replacing response probabilities that require numerical integration with estimators obtained by Monte Carlo simulation. This method of simulated moments (MSM) does not require precise estimates of these probabilities for consistency and asymptotic normality, relying instead on the law of large numbers operating across observations to control simulation error, and hence can use simulations of practical size. The method is useful for models such as high-dimensional multinomial probit (MNP), where computation has restricted applications.

A method of simulated moments for estimation of discrete response models without numerical integration

Nonlinear Programming: A Unified Approach

Encompassing all the major topics students will encounter in courses on the subject, the authors teach both the underlying mathematical foundations and how these ideas are implemented in practice. They illustrate all the concepts with both worked examples and plenty of exercises, and, in addition, provide software so that students can try out numerical methods and so hone their skills in interpreting the results. As a result, this will make an ideal textbook for all those coming to the subject for the first time. Authors' note: A problem recently found with the software is due to a bug in Formula One, the third party commercial software package that was used for the development of the interface. It occurs when the date, currency, etc. format is set to a non-United States version. Please try setting your computer date/currency option to the United States option . The new version of Formula One, when ready, will be posted on Www.

Linear Programming 1: Introduction

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.

Three digit accurate multiple normal probabilities

Random Number Generators and Simulation

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 ...

Computing Multivariate Normal Probabilities: A New Look

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.

Uniform random number generators for parallel computers

http://link.springer.com/content/pdf/10.1007/978-3-642-61370-8_7.pdf

István Deák

Papers

Three digit accurate multiple normal probabilities

Random Number Generators and Simulation

Computing Multivariate Normal Probabilities: A New Look

Uniform random number generators for parallel computers

Multidimensional Integration and Stochastic Programming