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Outline Why another . . . Problem classes Formulation of problems Case studies Algorithms Organization Level of development Software Additional materials Conclusion Home Page Title Page

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  • Outline

Why another . . . Problem classes Formulation of problems Case studies Algorithms Organization Level of development Software Additional materials Conclusion Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 1 of 12 Go Back Full Screen Close Quit

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Outline Why another . . . Problem classes Formulation of problems Case studies Algorithms Organization Level of development Software Additional materials Conclusion Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 2 of 12 Go Back Full Screen Close Quit

1. Outline

  • Why another optimization text?
  • Problem classes.
  • Formulation of problems.
  • Case studies.
  • Algorithms.
  • Organization.
  • Level of development.
  • Software.
  • Additional materials.
  • Conclusion.
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Outline Why another . . . Problem classes Formulation of problems Case studies Algorithms Organization Level of development Software Additional materials Conclusion Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 3 of 12 Go Back Full Screen Close Quit

2. Why another optimization text?

  • Many texts focus on the design of algorithms.
  • Many engineering students are involved with formu-

lating a problem: – expectation is to utilize existing algorithms and software for solution.

  • The “scarce resource” is increasingly in formulation,

not hardware or optimization software itself.

  • This book focuses on formulation of problems.
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3. Problem classes

  • Continuous variables and functions.
  • Incrementally defines and discusses:
  • 1. linear systems of equations,
  • 2. non-linear systems of equations,
  • 3. unconstrained optimization,
  • 4. equality-constrained optimization,
  • 5. inequality-constrained optimization.
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4. Formulation of problems

  • The book presents engineering applications through a

series of fourteen detailed case studies.

  • The case studies illustrate:

– formulation of simultaneous equations and opti- mization problems, – transformation of problem formulations, – solution of problems with existing general-purpose software, and – incremental development of formulations.

  • Simultaneous equations problems are covered in detail

since many signal processing and other engineering applications involve the solution of equations. – Solution of optimality conditions for optimization problems builds directly on solution of simultane-

  • us equations.
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5. Case studies

Linear equations Analysis of a direct current linear circuit

❄ ◗◗◗ ◗ s

Discrete-time linear system Non-linear equations Direct current non-linear circuit Electric power system

❄ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✌

Unconstrained

  • ptimization

Multi-variate linear regression

✲ ❇ ❇ ❇ ❇ ❇ ❇ ❇ ❇ ❇ ❇ ❇ ◆

Power system state estimation

❄

Equality- constrained

  • ptimization

❄

Least-cost production State estimation zero injection buses Inequality- constrained

  • ptimization

Production with capacity constraints

❄

Routing in a data network Least absolute value estimation Pattern classification Sizing of gate interconnects Optimal power flow

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6. Algorithms

  • One or two exemplar algorithms are introduced for

each problem class to illustrate the issues that arise in formulating problems.

  • Emphasize:

– monotonicity, – convexity, – problem transformations, – symmetry, and – sparsity.

  • Avoid details that are not prominent in problem for-

mulation: – variations and extensions introduced briefly.

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7. Organization

  • Three introductory chapters outline the problem

classes and discuss problem transformations.

  • The remaining chapters are organized in five Parts.
  • Each Part deals with a problem class and consists of

chapters describing: – formulation of at least two case studies, – algorithms to solve the problem class, – sensitivity analysis, and – solution of the case studies.

  • Each chapter has a number of homework exercises:

– Over three hundred pages of homework solutions available to instructors.

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8. Level of development

  • Aimed at incoming graduate students or senior un-

dergraduates.

  • Formal discussion in definition–theorem–proof style.
  • Complemented by:

– considerable discussion, – many worked examples, and – about 200 figures.

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9. Software

  • The Matlab Optimization Toolbox is used in some
  • f the homework exercises.
  • Other frameworks are possibly better suited to formu-

lation and solution of optimization problems.

  • Matlab is used by many engineering students in

their research: – minimizes the “start-up” costs of learning new packages, and – enables direct incorporation of optimization formu- lations into research projects.

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10. Additional materials

  • Available from www.cambridge.org/9780521855648
  • 1. Mathematical background.
  • 2. Proofs of results.
  • 3. Slides that I use in teaching this course.
  • 4. Over four hundred pages of homework solutions avail-

able to instructors.

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11. Conclusion

  • New book on solving equations and continuous opti-

mization.

  • Emphasizes formulation of problems and transforma-

tions.

  • For ordering information, visit the Home Page,

www.cambridge.org/9780521855648