Описание: 1. Optimal Control under Stochastic Uncertainty.- 2. Stochastic Optimization of Regulators.- 3. Optimal Open-Loop Control of Dynamic Systems under Stochastic Uncertainty.- 4. Construction of feedback control by means of homotopy methods.- 5. Constructions of Limit State Functions.- 6. Random Search Procedures for Global Optimization.- 7. Controlled Random Search under Uncertainty.- 8. Controlled Random Search Procedures for Global Optimization.- 9. Mathematical Model of Random Search Methods and Elementary Properties.- 10. Special Random Search Methods.- 11. Accessibility Theorems.- 12. Convergence Theorems.- 13. Convergence of Stationary Random Search Methods for Positive Success Probability.- 14. Random Search Methods of convergence order U(n-").- 15. Random Search Methods with a Linear Rate of Convergence.- 16. Success/Failure-driven Random Direction Procedures.- 17. Hybrid Methods.- 18. Solving optimization problems under stochastic uncertainty by Random Search Methods(RSM).
Описание: This book is an up-to-date, unified and rigorous treatment of theoretical, computational and applied research on Markov decision process models. The concentration of the book is on infinite-horizon discrete-time models, and it also discusses arbitrary state spaces, finite-horizon and continuous-time discrete-state models.
Описание: Lastly the constraints, expressed by equalities or inequalities between linear expressions, are often softer in reality that what their mathematical expression might let us believe, and infeasibility as detected by the linear programming techniques can often been coped with by making trade-offs with the real world.
Описание: Optimization problems whose constraints involve partial differential equations (PDEs) are relevant in many areas of technical, industrial, and economic app- cations. At the same time, they pose challenging mathematical research problems in numerical analysis and optimization. The present text is among the ?rst in the research literature addressing stochastic uncertainty in the context of PDE constrained optimization. The focus is on shape optimization for elastic bodies under stochastic loading. Analogies to ?nite dim- sional two-stage stochastic programming drive the treatment, with shapes taking the role of nonanticipative decisions.The main results concern level set-based s- chastic shape optimization with gradient methods involving shape and topological derivatives. The special structure of the elasticity PDE enables the numerical - lution of stochastic shape optimization problems with an arbitrary number of s- narios without increasing the computational effort signi?cantly. Both risk neutral and risk averse models are investigated. This monograph is based on a doctoral dissertation prepared during 2004-2008 at the Chair of Discrete Mathematics and Optimization in the Department of Ma- ematics of the University of Duisburg-Essen. The work was supported by the Deutsche Forschungsgemeinschaft (DFG) within the Priority Program "Optimi- tion with Partial Differential Equations." Rudiger Schultz Acknowledgments I owe a great deal to my supervisors, colleagues, and friends who have always supported, encouraged, andenlightenedmethroughtheirownresearch, comments, and questions.
Описание: Lastly the constraints, expressed by equalities or inequalities between linear expressions, are often softer in reality that what their mathematical expression might let us believe, and infeasibility as detected by the linear programming techniques can often been coped with by making trade-offs with the real world.
Описание: The papers cover a great variety of topics in probability, statistics, economics, stochastic optimization, control theory, regression analysis, simulation, stochastic programming, Markov decision process, application in the HIV context, and others.
Описание: Uwe Gotzes analyzes an approach to account for risk aversion in two-stage models based upon partial orders on the set of real random variables. He illustrates the superiority of the proposed decomposition method over standard solvers for example with numerical experiments with instances from energy investment.
Описание: This book presents the details of the BONUS algorithm and its real world applications in areas like sensor placement in large scale drinking water networks, sensor placement in advanced power systems, water management in power systems, and capacity expansion of energy systems.
Описание: This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations. It provides a gentle coverage of the theory of nonlinear expectations and related stochastic analysis. Many notions and results, for example, G-normal distribution, G-Brownian motion, G-Martingale representation theorem, and related stochastic calculus are first introduced or obtained by the author.This book is based on Shige Peng’s lecture notes for a series of lectures given at summer schools and universities worldwide. It starts with basic definitions of nonlinear expectations and their relation to coherent measures of risk, law of large numbers and central limit theorems under nonlinear expectations, and develops into stochastic integral and stochastic calculus under G-expectations. It ends with recent research topic on G-Martingale representation theorem and G-stochastic integral for locally integrable processes.With exercises to practice at the end of each chapter, this book can be used as a graduate textbook for students in probability theory and mathematical finance. Each chapter also concludes with a section Notes and Comments, which gives history and further references on the material covered in that chapter.Researchers and graduate students interested in probability theory and mathematical finance will find this book very useful.
Описание: This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations.
Описание: Chapter five contains examples of using ecological Life Cycle Assessment (LCA) - a relatively new method of environmental impact assessment - which help in preparing pro-ecological strategy, and which can lead to reducing the amount of wastes produced in the ArcelorMittal Steel Plant production processes.
