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Optimization

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Optimization

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This book is primarily aimed to be used in optimization courses at universities, engineering schools and business schools. It can be used by engineers, economists and others who work with optimization applications and optimization theory. The book describes how optimization models can be formulated and includes basic optimization theory, solution methods and practical use of the solver in Excel and the modeling language AMPL. The areas covered in the book are linear programming, network optim...

This book is primarily aimed to be used in optimization courses at universities, engineering schools and business schools. It can be used by engineers, economists and others who work with optimization applications and optimization theory. The book describes how optimization models can be formulated and includes basic optimization theory, solution methods and practical use of the solver in Excel and the modeling language AMPL. The areas covered in the book are linear programming, network optimization, nonlinear optimization, integer programming and dynamic programming. Models and methods are illustrated with a large number of examples and figures. This is the English version of the Swedish book Optimeringslära (2008). The two versions are equivalent to each other and can easily be used in the same course for teaching in both English and Swedish. There is also a supplementary exercise book (versions in both English and Swedish) with a large number of exercises and solutions.

    • 1
      1
      Introduction to Optimization
        • 1.1
          1
          What is optimization
        • 1.2
          3
          Areas of applications
        • 1.3
          8
          The optimization process
        • 1.4
          12
          Mathematical formulation and classification
    • 2
      15
      Introductional Examples and Basic Concepts
        • 2.1
          15
          Example linear programming – Fajo AB
        • 2.2
          21
          Example nonlinear optimization – Sport AB
        • 2.3
          25
          Example integer programming – Linbostäder
        • 2.4
          28
          Basic convexity analysis
        • 2.5
          33
          Search methods – a general description
        • 2.6
          39
          Basic complexity theory
    • 3
      43
      Modeling
        • 3.1
          43
          Index and summation
        • 3.2
          45
          Production planning
        • 3.3
          55
          Transport and distribution
        • 3.4
          63
          Blending problem
        • 3.5
          70
          Allocation models
    • 4
      77
      Linear Programming and the Simplex Method
        • 4.1
          77
          Mathematical characteristics of LP problems
        • 4.2
          80
          Standard form
        • 4.3
          83
          Basic solutions
        • 4.4
          87
          Change of basis
        • 4.5
          89
          The simplex method – an example
        • 4.6
          94
          The simplex method – general algorithm description
        • 4.7
          96
          Using simplex tableaux
        • 4.8
          97
          Algebraic description of the simplex method
        • 4.9
          100
          Finding a basic feasible solution
        • 4.10
          103
          Convergence and degeneration
    • 5
      107
      Sensitivity Analysis
        • 5.1
          108
          The sawmill Klinga – an illustrative example
        • 5.2
          110
          Relaxation and restriction
        • 5.3
          113
          Shadow prices and the connection to duality
        • 5.4
          117
          Interpretation of output from a software package
        • 5.5
          122
          Algebraic analysis of changes
        • 5.6
          129
          Perturbation of several coefficients simultaneously
    • 6
      133
      Duality
        • 6.1
          133
          Deriving and interpreting the dual problem
        • 6.2
          136
          Formulation of the dual problem
        • 6.3
          139
          Duality theory
    • 7
      147
      LP Extensions
        • 7.1
          147
          The simplex method for upper bounded variables
        • 7.2
          152
          Revised simplex method
        • 7.3
          158
          Dual simplex method
        • 7.4
          162
          Dantzig-Wolfe decomposition
        • 7.5
          168
          Interior point methods
    • 8
      181
      Network Optimization
        • 8.1
          181
          Problem review
        • 8.2
          183
          Basic concepts
        • 8.3
          187
          Minimum spanning tree
        • 8.4
          190
          Shortest path problems
        • 8.5
          202
          Project networks
        • 8.6
          206
          Minimum cost network flow problems
        • 8.7
          221
          The simplex method for network flow problems
    • 9
      235
      Introduction to Nonlinear Optimization
        • 9.1
          236
          Examples of nonlinear models
        • 9.2
          241
          Approximations of functions
        • 9.3
          244
          Convex analysis
    • 10
      257
      Methods for Unconstrained Nonlinear Optimization
        • 10.1
          259
          Steepest descent method
        • 10.2
          263
          Newton methods
        • 10.3
          266
          Extensions for Newton methods
        • 10.4
          268
          One-dimensional optimization
    • 11
      279
      Optimality Conditions for Nonlinear Problems
        • 11.1
          279
          Geometric interpretation of the KKT conditions
        • 11.2
          283
          KKT conditions derived using the Lagrangian function
        • 11.3
          287
          Necessary and sufficient conditions for optimality
        • 11.4
          290
          Formulation of the KKT conditions
    • 12
      295
      Methods for Constrained Nonlinear Optimization
        • 12.1
          296
          The Frank-Wolfe method
        • 12.2
          302
          Quadratic Programming
        • 12.3
          310
          Penalty function methods
        • 12.4
          316
          Barrier function methods
    • 13
      323
      Integer Programming Models
        • 13.1
          323
          What is an integer programming problem
        • 13.2
          330
          Knapsack problems
        • 13.3
          332
          Facility location
        • 13.4
          334
          Network design
        • 13.5
          337
          Assignment problems
        • 13.6
          339
          Generalized assignment problem
        • 13.7
          342
          Matching problem
        • 13.8
          344
          Set partitioning, set covering and set packing problems
        • 13.9
          349
          Sequencing problem
        • 13.10
          350
          Traveling salesman problem
        • 13.11
          355
          Route planning
    • 14
      361
      Solution Methods for Integer Programming Problems
        • 14.1
          361
          Overview of methods
        • 14.2
          364
          Optimality and relaxations
        • 14.3
          367
          To choose the right model
        • 14.4
          373
          Valid inequalities
        • 14.5
          377
          Cutting plane methods
        • 14.6
          386
          Column generation
    • 15
      393
      Branch and Bound methods
        • 15.1
          393
          Introduction
        • 15.2
          396
          General strategy for branch and bound
        • 15.3
          400
          The Land-Doig-Dakin algorithm
        • 15.4
          406
          Branch and bound methods for structured problems
        • 15.5
          413
          Extensions of branch and bound methods
    • 16
      421
      Heuristics
        • 16.1
          421
          Introduction
        • 16.2
          423
          Combinatorial formulations
        • 16.3
          424
          Constructive heuristics
        • 16.4
          438
          Local search
        • 16.5
          442
          Metaheuristics
        • 16.6
          451
          Approximation algorithms
    • 17
      455
      Lagrangian Duality and Lagrangian Relaxation
        • 17.1
          455
          Lagrangian duality
        • 17.2
          460
          Lagrangian relaxation
        • 17.3
          465
          Subgradient optimization
        • 17.4
          471
          Applications
    • 18
      481
      Dynamic Programming
        • 18.1
          481
          Introduction
        • 18.2
          482
          An initial example
        • 18.3
          484
          Network interpretation and Bellman’s equations
        • 18.4
          485
          General formulation
        • 18.5
          488
          Formulation of the shortest path problem
        • 18.6
          489
          Optimal order quantity
        • 18.7
          492
          Resource allocation
    • 19
      495
      Modeling System Excel
        • 19.1
          495
          Modeling of LP problems
        • 19.2
          501
          Modeling of IP problems
        • 19.3
          501
          Modeling of nonlinear problems
        • 19.4
          503
          Modeling of transportation problem
    • 20
      505
      Modeling System Ampl
        • 20.1
          505
          General modeling
        • 20.2
          513
          Nonlinear problem
        • 20.3
          514
          Inventory problem
        • 20.4
          517
          Blending problem
        • 20.5
          519
          Set partitioning models
        • 20.6
          521
          Minimum cost flow problems
        • 20.7
          522
          Generation of columns
        • 20.8
          526
          Heuristics in Ampl
    • 529
      A Further reading
    • Index

Information

Författare:
Jan Lundgren Mikael Rönnqvist Peter Värbrand
Språk:
Engelska
ISBN:
9789144053080
Utgivningsår:
2010
Artikelnummer:
33254-01
Upplaga:
Första
Sidantal:
548

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Optimization

Henningsson, Mathias m.fl.

This exercise book is a supplement to the book Optimization, written by the same authors. In an earlier Swedish version of the book (2003) some exe...

348 kr inkl. moms

Exkl. moms: 328 kr

Författare

Jan Lundgren

Jan Lundgren is a professor in Traffic Informatics at the Division of Communications and Transport Systems, Linköping University. His research is f...

Mikael Rönnqvist

Mikael Rönnqvist is a professor in Management Science at the Norwegian School of Economics and Business Administration. His research is focused on ...

Peter Värbrand

Peter Värbrand is a professor in Optimization at the Department of Science and Technology, Linköping University. His research is focused on applica...

Förlagskontakt

Jens Fredholm

Förläggare Teknik
Teknik, matematik och statistik
046-31 21 58 E-post

Fritjof Janson

Förlagskoordinator Kurslitteratur och Kompetensutveckling
046-31 22 57 E-post
 ;

This book is primarily aimed to be used in optimization courses at universities, engineering schools and business schools. It can be used by engineers, economists and others who work with optimization applications and optimization theory. The book describes how optimization models can be formulated and includes basic optimization theory, solution methods and practical use of the solver in Excel and the modeling language AMPL. The areas covered in the book are linear programming, network optim...

This book is primarily aimed to be used in optimization courses at universities, engineering schools and business schools. It can be used by engineers, economists and others who work with optimization applications and optimization theory. The book describes how optimization models can be formulated and includes basic optimization theory, solution methods and practical use of the solver in Excel and the modeling language AMPL. The areas covered in the book are linear programming, network optimization, nonlinear optimization, integer programming and dynamic programming. Models and methods are illustrated with a large number of examples and figures. This is the English version of the Swedish book Optimeringslära (2008). The two versions are equivalent to each other and can easily be used in the same course for teaching in both English and Swedish. There is also a supplementary exercise book (versions in both English and Swedish) with a large number of exercises and solutions.

Information

Författare:
Jan Lundgren Mikael Rönnqvist Peter Värbrand
Språk:
Engelska
ISBN:
9789144171524
Utgivningsår:
2010
Artikelnummer:
33254-SB01
Upplaga:
Första

Författare

Jan Lundgren

Jan Lundgren is a professor in Traffic Informatics at the Division of Communications and Transport Systems, Linköping University. His research is f...

Mikael Rönnqvist

Mikael Rönnqvist is a professor in Management Science at the Norwegian School of Economics and Business Administration. His research is focused on ...

Peter Värbrand

Peter Värbrand is a professor in Optimization at the Department of Science and Technology, Linköping University. His research is focused on applica...

Förlagskontakt

Jens Fredholm

Förläggare Teknik
Teknik, matematik och statistik
046-31 21 58 E-post

Fritjof Janson

Förlagskoordinator Kurslitteratur och Kompetensutveckling
046-31 22 57 E-post
 ;