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Chance constrained optimal beam design: Convex reformulation and probabilistic robust design

Jakub Kůdela, Pavel Popela (2018)

Kybernetika

In this paper, we are concerned with a civil engineering application of optimization, namely the optimal design of a loaded beam. The developed optimization model includes ODE-type constraints and chance constraints. We use the finite element method (FEM) for the approximation of the ODE constraints. We derive a convex reformulation that transforms the problem into a linear one and find its analytic solution. Afterwards, we impose chance constraints on the stress and the deflection of the beam....

Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems

Markos A. Katsoulakis, Petr Plecháč, Luc Rey-Bellet, Dimitrios K. Tsagkarogiannis (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

The primary objective of this work is to develop coarse-graining schemes for stochastic many-body microscopic models and quantify their effectiveness in terms of a priori and a posteriori error analysis. In this paper we focus on stochastic lattice systems of interacting particles at equilibrium. The proposed algorithms are derived from an initial coarse-grained approximation that is directly computable by Monte Carlo simulations, and the corresponding numerical error is calculated using the...

Combining System Dynamic Modeling and the Datar–Mathews Method for Analyzing Metal Mine Investments

Jyrki Savolainen, Mikael Collan, Pasi Luukka (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper presents how a dynamic system model can be used together with the Datar–Mathews real option analysis method for investment analysis of metal mining projects. The focus of the paper is on analyzing a project from the point of view of the project owner. The paper extends the Datar–Mathews real option analysis method by combining it with a dynamic system model. The model employs a dynamic discount rate that changes as the debt-level of the project changes. A numerical case illustration of...

Coupling a stochastic approximation version of EM with an MCMC procedure

Estelle Kuhn, Marc Lavielle (2004)

ESAIM: Probability and Statistics

The stochastic approximation version of EM (SAEM) proposed by Delyon et al. (1999) is a powerful alternative to EM when the E-step is intractable. Convergence of SAEM toward a maximum of the observed likelihood is established when the unobserved data are simulated at each iteration under the conditional distribution. We show that this very restrictive assumption can be weakened. Indeed, the results of Benveniste et al. for stochastic approximation with markovian perturbations are used to establish...

Coupling a stochastic approximation version of EM with an MCMC procedure

Estelle Kuhn, Marc Lavielle (2010)

ESAIM: Probability and Statistics

The stochastic approximation version of EM (SAEM) proposed by Delyon et al. (1999) is a powerful alternative to EM when the E-step is intractable. Convergence of SAEM toward a maximum of the observed likelihood is established when the unobserved data are simulated at each iteration under the conditional distribution. We show that this very restrictive assumption can be weakened. Indeed, the results of Benveniste et al. for stochastic approximation with Markovian perturbations are used to establish...

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