Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs

Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs

Author: Kurt Marti

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 195

ISBN-13: 3662025582

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In engineering and economics a certain vector of inputs or decisions must often be chosen, subject to some constraints, such that the expected costs arising from the deviation between the output of a stochastic linear system and a desired stochastic target vector are minimal. In many cases the loss function u is convex and the occuring random variables have, at least approximately, a joint discrete distribution. Concrete problems of this type are stochastic linear programs with recourse, portfolio optimization problems, error minimization and optimal design problems. In solving stochastic optimization problems of this type by standard optimization software, the main difficulty is that the objective function F and its derivatives are defined by multiple integrals. Hence, one wants to omit, as much as possible, the time-consuming computation of derivatives of F. Using the special structure of the problem, the mathematical foundations and several concrete methods for the computation of feasible descent directions, in a certain part of the feasible domain, are presented first, without any derivatives of the objective function F. It can also be used to support other methods for solving discretely distributed stochastic programs, especially large scale linear programming and stochastic approximation methods.


Book Synopsis Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs by : Kurt Marti

Download or read book Descent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs written by Kurt Marti and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: In engineering and economics a certain vector of inputs or decisions must often be chosen, subject to some constraints, such that the expected costs arising from the deviation between the output of a stochastic linear system and a desired stochastic target vector are minimal. In many cases the loss function u is convex and the occuring random variables have, at least approximately, a joint discrete distribution. Concrete problems of this type are stochastic linear programs with recourse, portfolio optimization problems, error minimization and optimal design problems. In solving stochastic optimization problems of this type by standard optimization software, the main difficulty is that the objective function F and its derivatives are defined by multiple integrals. Hence, one wants to omit, as much as possible, the time-consuming computation of derivatives of F. Using the special structure of the problem, the mathematical foundations and several concrete methods for the computation of feasible descent directions, in a certain part of the feasible domain, are presented first, without any derivatives of the objective function F. It can also be used to support other methods for solving discretely distributed stochastic programs, especially large scale linear programming and stochastic approximation methods.

Encyclopedia of Optimization

Encyclopedia of Optimization

Author: Christodoulos A. Floudas

Publisher: Springer Science & Business Media

Published: 2008-09-04

Total Pages: 4646

ISBN-13: 0387747583

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The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".


Book Synopsis Encyclopedia of Optimization by : Christodoulos A. Floudas

Download or read book Encyclopedia of Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2008-09-04 with total page 4646 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Stochastic Orders and Applications

Stochastic Orders and Applications

Author: Karl Mosler

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 385

ISBN-13: 3642499724

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A bibliography on stochastic orderings. Was there a real need for it? In a time of reference databases as the MathSci or the Science Citation Index or the Social Science Citation Index the answer seems to be negative. The reason we think that this bibliog raphy might be of some use stems from the frustration that we, as workers in the field, have often experienced by finding similar results being discovered and proved over and over in different journals of different disciplines with different levels of mathematical so phistication and accuracy and most of the times without cross references. Of course it would be very unfair to blame an economist, say, for not knowing a result in mathematical physics, or vice versa, especially when the problems and the languages are so far apart that it is often difficult to recognize the analogies even after further scrutiny. We hope that collecting the references on this topic, regardless of the area of application, will be of some help, at least to pinpoint the problem. We use the term stochastic ordering in a broad sense to denote any ordering relation on a space of probability measures. Questions that can be related to the idea of stochastic orderings are as old as probability itself. Think for instance of the problem of comparing two gambles in order to decide which one is more favorable.


Book Synopsis Stochastic Orders and Applications by : Karl Mosler

Download or read book Stochastic Orders and Applications written by Karl Mosler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: A bibliography on stochastic orderings. Was there a real need for it? In a time of reference databases as the MathSci or the Science Citation Index or the Social Science Citation Index the answer seems to be negative. The reason we think that this bibliog raphy might be of some use stems from the frustration that we, as workers in the field, have often experienced by finding similar results being discovered and proved over and over in different journals of different disciplines with different levels of mathematical so phistication and accuracy and most of the times without cross references. Of course it would be very unfair to blame an economist, say, for not knowing a result in mathematical physics, or vice versa, especially when the problems and the languages are so far apart that it is often difficult to recognize the analogies even after further scrutiny. We hope that collecting the references on this topic, regardless of the area of application, will be of some help, at least to pinpoint the problem. We use the term stochastic ordering in a broad sense to denote any ordering relation on a space of probability measures. Questions that can be related to the idea of stochastic orderings are as old as probability itself. Think for instance of the problem of comparing two gambles in order to decide which one is more favorable.

Two-Person Bargaining Experiments with Incomplete Information

Two-Person Bargaining Experiments with Incomplete Information

Author: Bettina Kuon

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 305

ISBN-13: 3642487777

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Think of the following situation: A project yielding a gross profit of 100 is offered to two firms. The project can only be conducted by a cooperation of the two firms. No firm is able to conduct the project alone. In order to receive the project the firms have to agree on the allocation of the gross profit. Each of both firms has an alternative project it conducts in case the joint project is not realized. The profitability of an allocation of the joint gross profit for a firm depends on the gross profit from its alternative project. The gross profit from an alternative project can be either 0 (low alternative value) or O


Book Synopsis Two-Person Bargaining Experiments with Incomplete Information by : Bettina Kuon

Download or read book Two-Person Bargaining Experiments with Incomplete Information written by Bettina Kuon and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Think of the following situation: A project yielding a gross profit of 100 is offered to two firms. The project can only be conducted by a cooperation of the two firms. No firm is able to conduct the project alone. In order to receive the project the firms have to agree on the allocation of the gross profit. Each of both firms has an alternative project it conducts in case the joint project is not realized. The profitability of an allocation of the joint gross profit for a firm depends on the gross profit from its alternative project. The gross profit from an alternative project can be either 0 (low alternative value) or O

Production Planning in Automated Manufacturing

Production Planning in Automated Manufacturing

Author: Yves Crama

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 212

ISBN-13: 3662004593

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In this book quantitative approaches are proposed for production planning problems in automated manufacturing. In particular techniques from operations research/combinatorial optimization provide ways to tackle these problems. Special attention is devoted to the efficient use of tools in production planning for automated manufacturing systems. The book presents models and tests solution strategies for different kinds of production decisions. A case study in the manufacturing of printed circuit boards highlights the methodology. This book will help understand the nature of production planning problems emerging in automated manufacturing and show how techniques from operations research may contribute to their solution.


Book Synopsis Production Planning in Automated Manufacturing by : Yves Crama

Download or read book Production Planning in Automated Manufacturing written by Yves Crama and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book quantitative approaches are proposed for production planning problems in automated manufacturing. In particular techniques from operations research/combinatorial optimization provide ways to tackle these problems. Special attention is devoted to the efficient use of tools in production planning for automated manufacturing systems. The book presents models and tests solution strategies for different kinds of production decisions. A case study in the manufacturing of printed circuit boards highlights the methodology. This book will help understand the nature of production planning problems emerging in automated manufacturing and show how techniques from operations research may contribute to their solution.

Resource-Constrained Project Scheduling

Resource-Constrained Project Scheduling

Author: Arno Sprecher

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 157

ISBN-13: 3642483976

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Within a project human and non-human resources are pulled together in a tempo raray organization in order to achieve a predefined goal (d. [20], p. 187). That is, in contrast to manufacturing management, project management is directed to an end. One major function of project management is the scheduling of the project. Project scheduling is the time-based arrangement of the activities comprising the project subject to precedence-, time-and resource-constraints (d. [4], p. 170). In the 1950's the standard methods MPM (Metra Potential Method) and CPM (Cri tical Path Method) were developed. Given deterministic durations and precedence constraints the minimum project length, time windows for the start times and critical paths can be calculated. At the same time another group of researchers developed the Program Evaluation and Review Technique (PERT) (d. [19], [73] and [90]). In contrast to MPM and CPM, random variables describe the activity durations. Based on the optimistic, most likely and pessimistic estimations of the activity durations an assumed Beta distribution is derived in order to calculate the distribution of the project duration, the critical events, the distribution of earliest and latest occurence of an event, the distribution of the slack of the events and the probability of exceeding a date. By the time the estimates of the distributions have been improved (d. e.g. [52] and [56]). Nevertheless, there are some points of critique concerning the estimation of the resulting distributions and probabilities (d. e.g. [48], [49] and [50]).


Book Synopsis Resource-Constrained Project Scheduling by : Arno Sprecher

Download or read book Resource-Constrained Project Scheduling written by Arno Sprecher and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within a project human and non-human resources are pulled together in a tempo raray organization in order to achieve a predefined goal (d. [20], p. 187). That is, in contrast to manufacturing management, project management is directed to an end. One major function of project management is the scheduling of the project. Project scheduling is the time-based arrangement of the activities comprising the project subject to precedence-, time-and resource-constraints (d. [4], p. 170). In the 1950's the standard methods MPM (Metra Potential Method) and CPM (Cri tical Path Method) were developed. Given deterministic durations and precedence constraints the minimum project length, time windows for the start times and critical paths can be calculated. At the same time another group of researchers developed the Program Evaluation and Review Technique (PERT) (d. [19], [73] and [90]). In contrast to MPM and CPM, random variables describe the activity durations. Based on the optimistic, most likely and pessimistic estimations of the activity durations an assumed Beta distribution is derived in order to calculate the distribution of the project duration, the critical events, the distribution of earliest and latest occurence of an event, the distribution of the slack of the events and the probability of exceeding a date. By the time the estimates of the distributions have been improved (d. e.g. [52] and [56]). Nevertheless, there are some points of critique concerning the estimation of the resulting distributions and probabilities (d. e.g. [48], [49] and [50]).

An Integrated Approach in Production Planning and Scheduling

An Integrated Approach in Production Planning and Scheduling

Author: Stephane Dauzere-Peres

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 154

ISBN-13: 3642468047

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Production Management is a large field concerned with all the aspects related to production, from the very bottom decisions at the machine level, to the top-level strategic decisicns. In this book, we are concerned with production planning and scheduling aspects. Traditional production planning methodologies are based on a now widely ac cepted hierarchical decom?osition into several planning decision levels. The higher in the hierarchy, the more aggregate are the models and the more important are the decisions. In this book, we only consider the last two decision levels in the hierarchy, namely, the mid-term (or tacticaQ planning level and the short-term (or operationaQ scheduling level. In the literature and in practice, the decisions are taken in sequence and in a top-down approach from the highest level in the hierarchy to the bottom level. The decisions taken at some level in the hierarchy are constrained by those already taken at upper levels and in turn, must translate into feasible objectives for the next lower levels in the hierarchy. It is a common sense remark to say that the whole hierarchical decision process is coherent if the interactions between different levels in the hierarchy are taken into account so that a decision taken at some level in the hierarchy translates into a feasible objective for the next decision level in the hierarchy. However, and surpris ingly enough, this crucial consistency issue is rarely investigated and few results are available in the literature.


Book Synopsis An Integrated Approach in Production Planning and Scheduling by : Stephane Dauzere-Peres

Download or read book An Integrated Approach in Production Planning and Scheduling written by Stephane Dauzere-Peres and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Production Management is a large field concerned with all the aspects related to production, from the very bottom decisions at the machine level, to the top-level strategic decisicns. In this book, we are concerned with production planning and scheduling aspects. Traditional production planning methodologies are based on a now widely ac cepted hierarchical decom?osition into several planning decision levels. The higher in the hierarchy, the more aggregate are the models and the more important are the decisions. In this book, we only consider the last two decision levels in the hierarchy, namely, the mid-term (or tacticaQ planning level and the short-term (or operationaQ scheduling level. In the literature and in practice, the decisions are taken in sequence and in a top-down approach from the highest level in the hierarchy to the bottom level. The decisions taken at some level in the hierarchy are constrained by those already taken at upper levels and in turn, must translate into feasible objectives for the next lower levels in the hierarchy. It is a common sense remark to say that the whole hierarchical decision process is coherent if the interactions between different levels in the hierarchy are taken into account so that a decision taken at some level in the hierarchy translates into a feasible objective for the next decision level in the hierarchy. However, and surpris ingly enough, this crucial consistency issue is rarely investigated and few results are available in the literature.

Stochastic Optimization Methods

Stochastic Optimization Methods

Author: Kurt Marti

Publisher: Springer Nature

Published:

Total Pages: 389

ISBN-13: 3031400593

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Book Synopsis Stochastic Optimization Methods by : Kurt Marti

Download or read book Stochastic Optimization Methods written by Kurt Marti and published by Springer Nature. This book was released on with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to the Theory of Nonlinear Optimization

Introduction to the Theory of Nonlinear Optimization

Author: Johannes Jahn

Publisher: Springer Nature

Published: 2020-07-02

Total Pages: 325

ISBN-13: 3030427609

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This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.


Book Synopsis Introduction to the Theory of Nonlinear Optimization by : Johannes Jahn

Download or read book Introduction to the Theory of Nonlinear Optimization written by Johannes Jahn and published by Springer Nature. This book was released on 2020-07-02 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.

Imperfect General Equilibrium

Imperfect General Equilibrium

Author: Pier C. Nicola

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 176

ISBN-13: 3642483992

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Economic theory of the last fifty years has been dominated by the paradigm of General Equilibrium Theory, based on the scientific work of Walras-Pareto-Cassel-Wald-Hicks-Arrow-De breu-McKenzie. Some of its grounding assumptions are: all prices are fully flexible; an auctioneer appropriately manipulates all prices according to the law of supply and demand; every con sumer has only one budget constraint; all agents are perfectly informed; no actions are taken by agents before a vector of prices has been found such that all markets clear. Indeed, when all markets clear every agent can implement her/his chosen (opti mal) action and nobody is urged to change his/her decisions. Under these assumptions it is generally said that in a (one pe riod, competitive) general equilibrium model there is no place for money. The present monograph takes general equilibrium as the ba sis on which to build the model presented. But its first aim is to completely dispense with the Walrasian auctioneer by giving firms the task of choosing their output price~ period after period.


Book Synopsis Imperfect General Equilibrium by : Pier C. Nicola

Download or read book Imperfect General Equilibrium written by Pier C. Nicola and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Economic theory of the last fifty years has been dominated by the paradigm of General Equilibrium Theory, based on the scientific work of Walras-Pareto-Cassel-Wald-Hicks-Arrow-De breu-McKenzie. Some of its grounding assumptions are: all prices are fully flexible; an auctioneer appropriately manipulates all prices according to the law of supply and demand; every con sumer has only one budget constraint; all agents are perfectly informed; no actions are taken by agents before a vector of prices has been found such that all markets clear. Indeed, when all markets clear every agent can implement her/his chosen (opti mal) action and nobody is urged to change his/her decisions. Under these assumptions it is generally said that in a (one pe riod, competitive) general equilibrium model there is no place for money. The present monograph takes general equilibrium as the ba sis on which to build the model presented. But its first aim is to completely dispense with the Walrasian auctioneer by giving firms the task of choosing their output price~ period after period.