Rios Neto, Atair Pinto, Ricardo L. U. F.

A stochastic approach is proposed to generate a direct search procedure where errors in the constraints are inherently treated. The objective is to have the possibility of directly considering the relative accuracy in the satisfaction of constraints, when one is numerically solving a nonlinear constrained optimization problem. This is done by addin...

Gitman, Michael B. Trusov, Peter V. Fedoseev, Sergei A.
Published in
Korean Journal of Computational & Applied Mathematics

In the present paper we consider a problem of choosing the rational way to carry on the metal processing (the problem of stochastic optimization) and the problem of determing the unknown characteristics of parameters described with random variables.

Deshouillers, Jean-Marc Freiman, Gregory A. Yudin, Alexander A.
Published in
Journal of Theoretical Probability

We derive an upper bound for the concentration of the sum of i.i.d. random variables with values in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{Z}^d$$ \end...

Medard, Muriel Tsitsiklis, John N. Bertsekas, Dimitri P. Abou Faycal, Ibrahim C. (Ibrahim Chafik)...

Modeling, quantification, and analysis of uncertainty. Formulation and solution in sample space. Random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference. Interpretations, applications, and lecture demonstrations. Meets with graduate ...

Farahmand, K.
Published in
Journal of Theoretical Probability

There is both mathematical and physical interest in the behaviour of the polynomial of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$a_0 + a_1 (_{\text{1}}^...

Introduction to probability, statistical mechanics, and thermodynamics. Random variables, joint and conditional probability densities, and functions of a random variable. Concepts of macroscopic variables and thermodynamic equilibrium, fundamental assumption of statistical mechanics, microcanonical and canonical ensembles. First, second, and third ...

Yang, R.J. Gu, L.
Published in
Structural and Multidisciplinary Optimization

Traditional reliability-based design optimization (RBDO) requires a double loop iteration process. The inner optimization loop is to find the most probable point (MPP) and the outer is the regular optimization loop to optimize the RBDO problem with reliability objectives or constraints. It is well known that the computation can be prohibitive when ...

Rosenholtz, Ruth

This course emphasizes statistics as a powerful tool for studying complex issues in behavioral and biological sciences, and explores the limitations of statistics as a method of inquiry. The course covers descriptive statistics, probability and random variables, inferential statistics, and basic issues in experimental design. Techniques introduced ...

Introduction to probability, statistical mechanics, and thermodynamics. Random variables, joint and conditional probability densities, and functions of a random variable. Concepts of macroscopic variables and thermodynamic equilibrium, fundamental assumption of statistical mechanics, microcanonical and canonical ensembles. First, second, and third ...

Bertsekas, Dimitri Tsitsiklis, John Médard, Muriel

This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability...