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Applying Quantile Optimization Techniques To Some Class Of Probablistic Constrained Programming Problem
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Book Synopsis APPLYING QUANTILE OPTIMIZATION TECHNIQUES TO SOME CLASS OF PROBABLISTIC CONSTRAINED PROGRAMMING PROBLEM by : ANDREI I. KIBZUN AND ANDREI V. NAUMOV
Download or read book APPLYING QUANTILE OPTIMIZATION TECHNIQUES TO SOME CLASS OF PROBABLISTIC CONSTRAINED PROGRAMMING PROBLEM written by ANDREI I. KIBZUN AND ANDREI V. NAUMOV and published by . This book was released on 1992 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Probabilistic Constrained Optimization by : Stanislav Uryasev
Download or read book Probabilistic Constrained Optimization written by Stanislav Uryasev and published by Springer Science & Business Media. This book was released on 2000-11-30 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic and percentile/quantile functions play an important role in several applications, such as finance (Value-at-Risk), nuclear safety, and the environment. Recently, significant advances have been made in sensitivity analysis and optimization of probabilistic functions, which is the basis for construction of new efficient approaches. This book presents the state of the art in the theory of optimization of probabilistic functions and several engineering and finance applications, including material flow systems, production planning, Value-at-Risk, asset and liability management, and optimal trading strategies for financial derivatives (options). Audience: The book is a valuable source of information for faculty, students, researchers, and practitioners in financial engineering, operation research, optimization, computer science, and related areas.
Book Synopsis QUANTILE OPTIMIZATION TECHNIQUES WITH APPLICATION TO CHANCE CONSTRAINED PROBLEM FOR WATER-SUPPLY SYSTEM DESIGN by : ANDREI V. KIEZUN AND ANDREI V HAUMOV
Download or read book QUANTILE OPTIMIZATION TECHNIQUES WITH APPLICATION TO CHANCE CONSTRAINED PROBLEM FOR WATER-SUPPLY SYSTEM DESIGN written by ANDREI V. KIEZUN AND ANDREI V HAUMOV and published by . This book was released on 1992 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis SOME RESULTS CONCERNING AN APPLICATION OF THE QUANTILE OPTRIMIZATION THEORY by : ANDREI V. NAUMOV
Download or read book SOME RESULTS CONCERNING AN APPLICATION OF THE QUANTILE OPTRIMIZATION THEORY written by ANDREI V. NAUMOV and published by . This book was released on 1992 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computation in Constrained Stochastic Model Predictive Control of Linear Systems by : Minyong Shin
Download or read book Computation in Constrained Stochastic Model Predictive Control of Linear Systems written by Minyong Shin and published by Stanford University. This book was released on 2011 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite its sub-optimality, Model Predictive Control (MPC) has received much attention over the recent decades due to its ability to handle constraints. In particular, stochastic MPC, which includes uncertainty in the system dynamics, is one of the most active recent research topics in MPC. In this dissertation, we focus on (1) increasing computation speed of constrained stochastic MPC of linear systems with additive noise and, (2) improving the accuracy of an approximate solution involving systems with additive and multiplicative noise. Constrained MPC for linear systems with additive noise has been successfully formulated as a semidefinite programming problem (SDP) using the Youla parameterization or innovation feedback and linear matrix inequalities. Unfortunately, this method can be prohibitively slow even for problems with moderate size state. Thus, in this thesis we develop an interior point algorithm which can more efficiently solve the problem. This algorithm converts the stochastic problem into a deterministic one using the mean and the covariance matrix as the system state and using affine feedback. A line search interior point method is then directly applied to the nonlinear deterministic optimization problem. In the process, we take advantage of a recursive structure that appears when a control problem is solved via the line search interior point method in order to decrease the algorithmic complexity of the solution. We compare the computation time and complexity of our algorithm against an SDP solver. The second part of the dissertation deals with systems with additive and multiplicative noise under probabilistic constraints. This class of systems differs from the additive noise case in that the probability distribution of a state is neither Gaussian nor known in closed form. This causes a problem when the probability constraints are dealt with. In previous studies, this problem has been tackled by approximating the state as a Gaussian random variable or by approximating the probability bound as an ellipsoid. In this dissertation, we use the Cornish-Fisher expansion to approximate the probability bounds of the constraints. Since the Cornish-Fisher expansion utilizes quantile values with the first several moments, the probabilistic constraints have the same form as those in the additive noise case when the constraints are converted to deterministic ones. This makes the procedure smooth when we apply the developed algorithm to a linear system with multiplicative noise. Moreover, we can easily extend the application of the algorithm to a linear system with additive plus multiplicative noise.
Book Synopsis Probabilistic Covering Problems by : Feng Qiu
Download or read book Probabilistic Covering Problems written by Feng Qiu and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation studies optimization problems that involve probabilistic covering constraints. A probabilistic constraint evaluates and requires that the probability that a set of constraints involving random coefficients with known distributions hold satisfy a minimum requirement. A covering constraint involves a linear inequality on non-negative variables with a greater or equal to sign and non-negative coefficients. A variety of applications, such as set cover problems, node/edge cover problems, crew scheduling, production planning, facility location, and machine learning, in uncertain settings involve probabilistic covering constraints. In the first part of this dissertation we consider probabilistic covering linear programs. Using the sampling average approximation (SAA) framework, a probabilistic covering linear program can be approximated by a covering k-violation linear program (CKVLP), a deterministic covering linear program in which at most k constraints are allowed to be violated. We show that CKVLP is strongly NP-hard. Then, to improve the performance of standard mixed-integer programming (MIP) based schemes for CKVLP, we (i) introduce and analyze a coefficient strengthening scheme, (ii) adapt and analyze an existing cutting plane technique, and (iii) present a branching technique. Through computational experiments, we empirically verify that these techniques are significantly effective in improving solution times over the CPLEX MIP solver. In particular, we observe that the proposed schemes can cut down solution times from as much as six days to under four hours in some instances. We also developed valid inequalities arising from two subsets of the constraints in the original formulation. When incorporating them with a modified coefficient strengthening procedure, we are able to solve a difficult probabilistic portfolio optimization instance listed in MIPLIB 2010, which cannot be solved by existing approaches. In the second part of this dissertation we study a class of probabilistic 0-1 covering problems, namely probabilistic k-cover problems. A probabilistic k-cover problem is a stochastic version of a set k-cover problem, which is to seek a collection of subsets with a minimal cost whose union covers each element in the set at least k times. In a stochastic setting, the coefficients of the covering constraints are modeled as Bernoulli random variables, and the probabilistic constraint imposes a minimal requirement on the probability of k-coverage. To account for absence of full distributional information, we define a general ambiguous k-cover set, which is ``distributionally-robust." Using a classical linear program (called the Boolean LP) to compute the probability of events, we develop an exact deterministic reformulation to this ambiguous k-cover problem. However, since the boolean model consists of exponential number of auxiliary variables, and hence not useful in practice, we use two linear program based bounds on the probability that at least k events occur, which can be obtained by aggregating the variables and constraints of the Boolean model, to develop tractable deterministic approximations to the ambiguous k-cover set. We derive new valid inequalities that can be used to strengthen the linear programming based lower bounds. Numerical results show that these new inequalities significantly improve the probability bounds. To use standard MIP solvers, we linearize the multi-linear terms in the approximations and develop mixed-integer linear programming formulations. We conduct computational experiments to demonstrate the quality of the deterministic reformulations in terms of cost effectiveness and solution robustness. To demonstrate the usefulness of the modeling technique developed for probabilistic k-cover problems, we formulate a number of problems that have up till now only been studied under data independence assumption and we also introduce a new applications that can be modeled using the probabilistic k-cover model.
Book Synopsis Computation in Constrained Stochastic Model Predictive Control of Linear Systems by : Minyong Shin
Download or read book Computation in Constrained Stochastic Model Predictive Control of Linear Systems written by Minyong Shin and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite its sub-optimality, Model Predictive Control (MPC) has received much attention over the recent decades due to its ability to handle constraints. In particular, stochastic MPC, which includes uncertainty in the system dynamics, is one of the most active recent research topics in MPC. In this dissertation, we focus on (1) increasing computation speed of constrained stochastic MPC of linear systems with additive noise and, (2) improving the accuracy of an approximate solution involving systems with additive and multiplicative noise. Constrained MPC for linear systems with additive noise has been successfully formulated as a semidefinite programming problem (SDP) using the Youla parameterization or innovation feedback and linear matrix inequalities. Unfortunately, this method can be prohibitively slow even for problems with moderate size state. Thus, in this thesis we develop an interior point algorithm which can more efficiently solve the problem. This algorithm converts the stochastic problem into a deterministic one using the mean and the covariance matrix as the system state and using affine feedback. A line search interior point method is then directly applied to the nonlinear deterministic optimization problem. In the process, we take advantage of a recursive structure that appears when a control problem is solved via the line search interior point method in order to decrease the algorithmic complexity of the solution. We compare the computation time and complexity of our algorithm against an SDP solver. The second part of the dissertation deals with systems with additive and multiplicative noise under probabilistic constraints. This class of systems differs from the additive noise case in that the probability distribution of a state is neither Gaussian nor known in closed form. This causes a problem when the probability constraints are dealt with. In previous studies, this problem has been tackled by approximating the state as a Gaussian random variable or by approximating the probability bound as an ellipsoid. In this dissertation, we use the Cornish-Fisher expansion to approximate the probability bounds of the constraints. Since the Cornish-Fisher expansion utilizes quantile values with the first several moments, the probabilistic constraints have the same form as those in the additive noise case when the constraints are converted to deterministic ones. This makes the procedure smooth when we apply the developed algorithm to a linear system with multiplicative noise. Moreover, we can easily extend the application of the algorithm to a linear system with additive plus multiplicative noise.
Book Synopsis Decision Processes by Using Bivariate Normal Quantile Pairs by : N. C. Das
Download or read book Decision Processes by Using Bivariate Normal Quantile Pairs written by N. C. Das and published by Springer. This book was released on 2015-10-07 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses equi-quantile values and their use in generating decision alternatives under the twofold complexities of uncertainty and dependence, offering scope for surrogating between two alternative portfolios when they are correlated. The book begins with a discussion on components of rationality and learning models as indispensable concepts in decision-making processes. It identifies three-fold complexities in such processes: uncertainty, dependence and dynamism. The book is a novel attempt to seek tangible solutions for such decision problems. To do so, four hundred tables of bi-quantile pairs are presented for carefully chosen grids. In fact, it is a two-variable generalization of the inverse normal integral table, which is used in obtaining bivariate normal quantile pairs for the given values of probability and correlation. When making decisions, only two of them have to be taken at a time. These tables are essential tools for decision-making under risk and dependence, and offer scope for delving up to a single step of dynamism. The book subsequently addresses averments dealing with applications and advantages. The content is useful to empirical scientists and risk-oriented decision makers who are often required to make choices on the basis of pairs of variables. The book also helps simulators seeking valid confidence intervals for their estimates, and particle physicists looking for condensed confidence intervals for Higgs–Boson utilizing the Bose–Einstein correlation given the magnitude of such correlations. Entrepreneurs and investors as well as students of management, statistics, economics and econometrics, psychology, psychometrics and psychographics, social sciences, geographic information system, geology, agricultural and veterinary sciences, medical sciences and diagnostics, and remote sensing will also find the book very useful.
Book Synopsis Integrating Probabilistic Reasoning with Constraint Satisfaction by : Eric I-Hung Hsu
Download or read book Integrating Probabilistic Reasoning with Constraint Satisfaction written by Eric I-Hung Hsu and published by . This book was released on 2011 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: We hypothesize and confirm that probabilistic reasoning is closely related to constraint satisfaction at a formal level, and that this relationship yields effective algorithms for guiding constraint satisfaction and constraint optimization solvers.Further, for MaxSAT we present an equivalent transformation" process that normalizes the weights in constraint optimization problems, in order to encourage prunings of the search tree during branch-and-bound search. To control such computationally expensive processes, we determine promising situations for using them throughout the course of an individual search process. We accomplish this using a reinforcement learning-based control module that seeks a principled balance between the exploration of new strategies and the exploitation of existing experiences.By taking a unified view of probabilistic inference and constraint reasoning in terms of graphical models, we first associate a number of formalisms and techniques between the two areas. For instance, we characterize search and inference in constraint reasoning as summation and multiplication (or disjunction and conjunction) in the probabilistic space; necessary but insufficient consistency conditions for solutions to constraint problems (like arc-consistency) mirror approximate objective functions over probability distributions (like the Bethe free energy); and the polytope of feasible points for marginal probabilities represents the linear relaxation of a particular constraint satisfaction problem.While such insights synthesize an assortment of existing formalisms from varied research communities, they also yield an entirely novel set of "bias estimation" techniques that contribute to a growing body of research on applying probabilistic methods to constraint problems. In practical terms, these techniques estimate the percentage of solutions to a constraint satisfaction or optimization problem wherein a given variable is assigned a given value. By devising search methods that incorporate such information as heuristic guidance for variable and value ordering, we are able to outperform existing solvers on problems of interest from constraint satisfaction and constraint optimization-as represented here by the SAT and MaxSAT problems.
Book Synopsis Lectures on Stochastic Programming by : Alexander Shapiro
Download or read book Lectures on Stochastic Programming written by Alexander Shapiro and published by SIAM. This book was released on 2009-01-01 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. Readers will find coverage of the basic concepts of modeling these problems, including recourse actions and the nonanticipativity principle. The book also includes the theory of two-stage and multistage stochastic programming problems; the current state of the theory on chance (probabilistic) constraints, including the structure of the problems, optimality theory, and duality; and statistical inference in and risk-averse approaches to stochastic programming.
Book Synopsis Numerical Methods for Probabilistic Constrained Optimization Problem where Random Variables Have Degenerate Continuous Distribution by : Olga Myndyuk
Download or read book Numerical Methods for Probabilistic Constrained Optimization Problem where Random Variables Have Degenerate Continuous Distribution written by Olga Myndyuk and published by . This book was released on 2016 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several probabilistic constrained problems (single commodity stochastic network design problem and water reservoir problem) are formulated and solved by use of different numerical methods. The distribution considered are degenerate normal and uniform distributions. The network design problem is to find optimal node and arc capacities under some deterministic and probabilistic constraints that ensure the satisfiability of all demands on a given probability level. The large number of feasibility inequalities is reduced to a much smaller number of them and an equivalent reformulation takes us to a specially structured semi-infinite LP. This, in turn, is solved by a combination of inner and outer algorithms providing us with both lower and upper bounds for the optimum at each iteration. The flood control and serially linked reservoir network design with consecutive k-out-of-n type reliability problems are formulated, simplified and solved. Alternative, derivative-free methods, are proposed and implemented. Various numerical examples are presented and solution methods software library is developed.
Download or read book The Engineering Index Annual written by and published by . This book was released on 1992 with total page 2264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its creation in 1884, Engineering Index has covered virtually every major engineering innovation from around the world. It serves as the historical record of virtually every major engineering innovation of the 20th century. Recent content is a vital resource for current awareness, new production information, technological forecasting and competitive intelligence. The world?s most comprehensive interdisciplinary engineering database, Engineering Index contains over 10.7 million records. Each year, over 500,000 new abstracts are added from over 5,000 scholarly journals, trade magazines, and conference proceedings. Coverage spans over 175 engineering disciplines from over 80 countries. Updated weekly.
Book Synopsis Statistical Postprocessing of Ensemble Forecasts by : Stéphane Vannitsem
Download or read book Statistical Postprocessing of Ensemble Forecasts written by Stéphane Vannitsem and published by Elsevier. This book was released on 2018-05-22 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Postprocessing of Ensemble Forecasts brings together chapters contributed by international subject-matter experts describing the current state of the art in the statistical postprocessing of ensemble forecasts. The book illustrates the use of these methods in several important applications including weather, hydrological and climate forecasts, and renewable energy forecasting. After an introductory section on ensemble forecasts and prediction systems, the second section of the book is devoted to exposition of the methods available for statistical postprocessing of ensemble forecasts: univariate and multivariate ensemble postprocessing are first reviewed by Wilks (Chapters 3), then Schefzik and Möller (Chapter 4), and the more specialized perspective necessary for postprocessing forecasts for extremes is presented by Friederichs, Wahl, and Buschow (Chapter 5). The second section concludes with a discussion of forecast verification methods devised specifically for evaluation of ensemble forecasts (Chapter 6 by Thorarinsdottir and Schuhen). The third section of this book is devoted to applications of ensemble postprocessing. Practical aspects of ensemble postprocessing are first detailed in Chapter 7 (Hamill), including an extended and illustrative case study. Chapters 8 (Hemri), 9 (Pinson and Messner), and 10 (Van Schaeybroeck and Vannitsem) discuss ensemble postprocessing specifically for hydrological applications, postprocessing in support of renewable energy applications, and postprocessing of long-range forecasts from months to decades. Finally, Chapter 11 (Messner) provides a guide to the ensemble-postprocessing software available in the R programming language, which should greatly help readers implement many of the ideas presented in this book. Edited by three experts with strong and complementary expertise in statistical postprocessing of ensemble forecasts, this book assesses the new and rapidly developing field of ensemble forecast postprocessing as an extension of the use of statistical corrections to traditional deterministic forecasts. Statistical Postprocessing of Ensemble Forecasts is an essential resource for researchers, operational practitioners, and students in weather, seasonal, and climate forecasting, as well as users of such forecasts in fields involving renewable energy, conventional energy, hydrology, environmental engineering, and agriculture.
Book Synopsis Integration of AI and OR Techniques in Constraint Programming by : Helmut Simonis
Download or read book Integration of AI and OR Techniques in Constraint Programming written by Helmut Simonis and published by Springer. This book was released on 2014-05-12 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the International Conference on the Integration of Artificial Intelligence (AI) and Operations Research (OR) Techniques in Constraint Programming, CPAIOR 2014, held in Cork, Ireland, in May 2014. The 33 papers presented in this volume were carefully reviewed and selected from 70 submissions. The papers focus on constraint programming and global constraints; scheduling modelling; encodings and SAT logistics; MIP; CSP and complexity; parallelism and search; and data mining and machine learning.
Book Synopsis Algorithms for Optimization by : Mykel J. Kochenderfer
Download or read book Algorithms for Optimization written by Mykel J. Kochenderfer and published by MIT Press. This book was released on 2019-03-12 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals.
Book Synopsis Probabilistic Constrained Programming by : János Mayer
Download or read book Probabilistic Constrained Programming written by János Mayer and published by . This book was released on 1988 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Programming written by and published by . This book was released on 1991 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
