Leonidas Sakalauskas

Nonlinear stochastic programming by Monte-Carlo estimators

Abstract Methods for solving stochastic programming (SP) problems by a finite series of Monte-Carlo samples are considered. The accuracy of solution is treated in a statistical manner, testing the hypothesis of optimality according to statistical criteria. The rule for adjusting the Monte-Carlo sample size is introduced to ensure the convergence and to find the solution of the SP problem using a reasonable number of Monte-Carlo trials. Issues of implementation of the developed approach in decision making and other applicable fields are considered too.

On the law of the iterated logarithm in open queueing networks

Abstract An open queueing network model in heavy traffic is developed. Such models are mathematical models of computer networks in heavy traffic. Laws of the iterated logarithm for the virtual waiting time of the customer in open queueing networks and homogeneous computer networks are proved.

Editorial: Optimization and intelligent decisions

Extension of optimization to decision‐making systems is challenging topic of research. This paper surveys the special journal issue on the subject “Optimization and intelligent decisions.” Papers on intelligent decision theory as well as on decision in economic systems are presented and discussed. Information technologies for web‐based intelligent systems environment, which offers generic, modular, flexible and scalable system solutions for information retrieval, extraction, fusion, knowledge discovery and intelligent decision support, might be a subject of future research extending optimization in decision‐making.

Application of statistical criteria to optimality testing in stochastic programming

Abstract In this paper the stochastic adaptive method has been developed to solve stochastic linear problems by a finite sequence of Monte‐Carlo sampling estimators. The method is grounded on adaptive regulation of the size of Monte‐Carlo samples and the statistical termination procedure, taking into consideration the statistical modeling error. Our approach distinguishes itself by treatment of the accuracy of the solution in a statistical manner, testing the hypothesis of optimality according to statistical criteria, and estimating confidence intervals of the objective and constraint functions. The adjustment of sample size, when it is taken inversely proportional to the square of the norm of the Monte‐Carlo estimate of the gradient, guarantees the convergence a. s. at a linear rate. We examine four estimators for stochastic gradient: by the differentiation of the integral with respect to x, the finite difference approach, the Simulated Perturbation Stochastic Approximation approach, the Likelihood Ratio...

Three parameter estimation of the Weibull distribution by order statistics

Abstract. In this paper, we consider the estimation of the three-parameter Weibull distribution. We construct numerical algorithms to estimate the location, scale and shape parameters by maximal likelihood and simplified analytical methods. Convergence of these algorithms is studied theoretically and by computer modeling. Computer modeling results confirm practical applicability of estimates proposed. Recommendations for implementation of the estimates are discussed, too. Results from simulation studies assessing the performance of our proposed method are included.

APPLICATION OF STOCHASTIC APPROXIMATION IN TECHNICAL DESIGN

AbstractIn this paper, we consider problems related to the implementation of Stochastic Approximation (SA) in technical design, namely, estimation of a stochastic gradient, improvement of convergence, stopping criteria of the algorithm, etc. The accuracy of solution and the termination of the algorithm are considered in a statistical way. We build a method for estimation of confidence interval of the objective function extremum and stopping of the algorithm according to order statistics of objective function values provided during optimization. We give some illustration examples of application of developed approach of SA to the optimal engineering design problems, too.

Nonlinear Stochastic Optimization by the Monte-Carlo Method

Methods for solving stochastic optimization problems by Monte-Carlo simulation are considered. The stoping and accuracy of the solutions is treated in a statistical manner, testing the hypothesis of optimality according to statistical criteria. A rule for adjusting the Monte-Carlo sample size is introduced to ensure the convergence and to find the solution of the stochastic opti- mization problem from acceptable volume of Monte-Carlo trials. The examples of application of the developed method to importance sampling and the Weber location problem are also considered.

Consistent Estimator of the Shape Parameter of Three-Dimensional Weibull Distribution

In this article, a new estimator for the shape parameter of the three-dimensional Weibull distribution is proposed using order statistics taken from a large scale data set. It is proved that this estimator has good properties, such as asymptotic unbiasedness and consistency. Computer modeling results corroborate practical applicability of the estimator proposed. Recommendations for implementating the estimator are discussed, as well. We investigate the properties of this estimator in large-scale data sets.

Wiki-Based Stochastic Programming and Statistical Modeling System for the Cloud

Scientific software is a special type of software because its quality has a huge impact on the quality of scientific conclusions and scientific progress. However, it is hard to ensure required quality of the software because of the misunderstandings between the scientists and the software engineers. In this paper, we present a system for improving the quality of scientific software using elements of wikinomics and cloud computing and its implementation details. The system enables scientists to collaborate and make direct evolution of the models, algorithms, and programs. WikiSPSM expands the limits of mathematical software.

Python for scientific computing education: Modeling of queueing systems

In this paper, we present the methodology for the introduction to scientific computing based on model-centered learning. We propose multiphase queueing systems as a basis for learning objects. We use Python and parallel programming for implementing the models and present the computer code and results of stochastic simulations.