Download or read book The Duality Between Expected Utility and Penalty in Stochastic Linear Programming written by A. Ben-Tai and published by . This book was released on 1983 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document studies the dual problem corresponding to a linear program in which the stochastic objective function is replaced by its expected utility, and discusses its relevance as a penalty method to a stochastically constrained dual linear program.
Download or read book Expected Utility Penalty Functions and Duality in Stochastic Nonlinear Programming Revised written by A. Ben-Tal and published by . This book was released on 1985 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document considers nonlinear programming problems with stochastic constraints. The Lagrangian corresponding to such problems has a stochastic part, which in this work is replaced by its certainty equivalent (in the sense of expected utility theory). It is shown that the deterministic surrogate problem thus obtained, contains a penalty function which penalized violation of the constraints in the mean. The dual problem is studied (for problems with stochastic righthand sides in the constraints) and a comprehensive duality theory is developed by introducing a new certainty equivalent concept, which possesses, for arbitrary utility functions, some of the properties that the classical certainty equivalent retains only for the exponential utility. Additional keywords: Minmax theorems; Convex functions; and Risk aversion. (Author).
Download or read book Duality in Stochastic Linear and Dynamic Programming written by Willem K. Klein Haneveld and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1985 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Programming written by András Prékopa and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic programming - the science that provides us with tools to design and control stochastic systems with the aid of mathematical programming techniques - lies at the intersection of statistics and mathematical programming. The book Stochastic Programming is a comprehensive introduction to the field and its basic mathematical tools. While the mathematics is of a high level, the developed models offer powerful applications, as revealed by the large number of examples presented. The material ranges form basic linear programming to algorithmic solutions of sophisticated systems problems and applications in water resources and power systems, shipbuilding, inventory control, etc. Audience: Students and researchers who need to solve practical and theoretical problems in operations research, mathematics, statistics, engineering, economics, insurance, finance, biology and environmental protection.
Download or read book Introduction to Stochastic Programming written by John R. Birge and published by Springer Science & Business Media. This book was released on 2011-06-15 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of stochastic programming is to find optimal decisions in problems which involve uncertain data. This field is currently developing rapidly with contributions from many disciplines including operations research, mathematics, and probability. At the same time, it is now being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors aim to present a broad overview of the main themes and methods of the subject. Its prime goal is to help students develop an intuition on how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems. In this extensively updated new edition there is more material on methods and examples including several new approaches for discrete variables, new results on risk measures in modeling and Monte Carlo sampling methods, a new chapter on relationships to other methods including approximate dynamic programming, robust optimization and online methods. The book is highly illustrated with chapter summaries and many examples and exercises. Students, researchers and practitioners in operations research and the optimization area will find it particularly of interest. Review of First Edition: "The discussion on modeling issues, the large number of examples used to illustrate the material, and the breadth of the coverage make 'Introduction to Stochastic Programming' an ideal textbook for the area." (Interfaces, 1998)
Download or read book The Entropic Penalty Approach to Stochastic Programming written by A. Ben-Tal and published by . This book was released on 1983 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new decision-theoretic approach to Nonlinear Programming Problems with stochastic constraints is introduced. The Stochastic Program (SP) is replaced by a Deterministic Program (DP) in which a term is added to the objective function to penalize solutions which are not feasible in the mean. The special feature of the author's approach is the choice of the penalty function P sub E, which is given in terms if the relative entropy functional, and is accordingly called entropic penalty. It is shown that P sub E has properties which make it suitable to treat stochastic programs. Some of these properties are derived via a dual representation independent. The dual representation is also used to express the Deterministric Problem (DP) as a saddle function problem. For problems in which the randomness occurs in the rhs of the constraints, it shown that the dual problem of (DP) is equivalent to Expected Utility Maximization of the classical Lagrangian dual function of (SP), with the utility being of the constant-risk-aversion type. Finally, mean-variance approximations of P sub E and the induced Approximate Deterministic Program are considered.
Download or read book Penalty Functions and Duality in Stochastic Programming Via Phi Divergence Functionals written by A. Ben-Tal and published by . This book was released on 1984 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers stochastically constrained nonlinear programming problems, A penalty type method is suggested as a deterministic surrogate. The penalty is constructed in terms of a 'distance' function between random variables, given a term of the phi-divergence functional (a generalization of the relative entropy). A duality theory is developed in which a general relation between phi-divergence and utility functions is revealed, via the conjugate transform, and a new type of certainty equivalent concept emerges. Additional keywords: computations; vector analysis.
Download or read book Systems and Management Science by Extremal Methods written by Fred Young Phillips and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, Systems and Management Science by Extremal Methods, is the second in a series dedicated to honoring and extending the work of Abraham Charnes. The first volume, entitled Extremal Methods and Systems Analysis (Springer Verlag, Berlin, 1980), was edited by A.V. Fiacco and K.O. Kortanek. Subtitled "An International Symposium on the Occasion of Abraham Charnes' Sixtieth Birthday," this first volume consisted of a selection from papers presented at a conference in honor of Professor Charnes held at The University of Texas at Austin in September 1977. This second volume consists of papers, to be described more fully below, that were presented in a similar 2 conference held at the IC Institute of The University of Texas at Austin, Texas, in October of 1987, to honor Dr. Charnes on his seventieth birthday. All these papers were written by scholars and scientists whose own work has been affected by the contributions of this distinguished scholar and educator over a long period of time.
Download or read book Stochastic Processes and Models in Operations Research written by Anbazhagan, Neelamegam and published by IGI Global. This book was released on 2016-03-24 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Decision-making is an important task no matter the industry. Operations research, as a discipline, helps alleviate decision-making problems through the extraction of reliable information related to the task at hand in order to come to a viable solution. Integrating stochastic processes into operations research and management can further aid in the decision-making process for industrial and management problems. Stochastic Processes and Models in Operations Research emphasizes mathematical tools and equations relevant for solving complex problems within business and industrial settings. This research-based publication aims to assist scholars, researchers, operations managers, and graduate-level students by providing comprehensive exposure to the concepts, trends, and technologies relevant to stochastic process modeling to solve operations research problems.
Download or read book Modeling with Stochastic Programming written by Alan J. King and published by Springer Science & Business Media. This book was released on 2012-06-19 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: While there are several texts on how to solve and analyze stochastic programs, this is the first text to address basic questions about how to model uncertainty, and how to reformulate a deterministic model so that it can be analyzed in a stochastic setting. This text would be suitable as a stand-alone or supplement for a second course in OR/MS or in optimization-oriented engineering disciplines where the instructor wants to explain where models come from and what the fundamental issues are. The book is easy-to-read, highly illustrated with lots of examples and discussions. It will be suitable for graduate students and researchers working in operations research, mathematics, engineering and related departments where there is interest in learning how to model uncertainty. Alan King is a Research Staff Member at IBM's Thomas J. Watson Research Center in New York. Stein W. Wallace is a Professor of Operational Research at Lancaster University Management School in England.
Download or read book A Study of Risk aversion and Duality in Stochastic Linear Programming written by Gerald J. La Cava and published by . This book was released on 1971 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Post Optimal Analysis in Linear Semi Infinite Optimization written by Miguel A. Goberna and published by Springer Science & Business Media. This book was released on 2014-01-06 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Post-Optimal Analysis in Linear Semi-Infinite Optimization examines the following topics in regards to linear semi-infinite optimization: modeling uncertainty, qualitative stability analysis, quantitative stability analysis and sensitivity analysis. Linear semi-infinite optimization (LSIO) deals with linear optimization problems where the dimension of the decision space or the number of constraints is infinite. The authors compare the post-optimal analysis with alternative approaches to uncertain LSIO problems and provide readers with criteria to choose the best way to model a given uncertain LSIO problem depending on the nature and quality of the data along with the available software. This work also contains open problems which readers will find intriguing a challenging. Post-Optimal Analysis in Linear Semi-Infinite Optimization is aimed toward researchers, graduate and post-graduate students of mathematics interested in optimization, parametric optimization and related topics.
Download or read book Government Reports Annual Index written by and published by . This book was released on 1984 with total page 1316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sections 1-2. Keyword Index.--Section 3. Personal author index.--Section 4. Corporate author index.-- Section 5. Contract/grant number index, NTIS order/report number index 1-E.--Section 6. NTIS order/report number index F-Z.
Download or read book Duality in Stochastic Linear and Dynamic Programming written by Willem K. Klein Haneveld and published by Springer. This book was released on 2014-03-12 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government Reports Annual Index Keyword A L written by and published by . This book was released on 1987 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Risk Averse Optimization and Control written by Darinka Dentcheva and published by Springer Nature. This book was released on with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt:
