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
Outline Why another . . . Problem classes Formulation of problems 1. Outline Case studies Algorithms Organization • Why another optimization text? Level of development Software • Problem classes. Additional materials Conclusion • Formulation of problems. • Case studies. Home Page Title Page • Algorithms. ◭◭ ◮◮ • Organization. ◭ ◮ • Level of development. Page 2 of 12 • Software. Go Back • Additional materials. Full Screen • Conclusion. Close Quit
Outline Why another . . . Problem classes Formulation of problems Case studies Algorithms Organization 2. Why another optimization Level of development Software text? Additional materials Conclusion • Many texts focus on the design of algorithms. Home Page • Many engineering students are involved with formu- lating a problem: Title Page ◭◭ ◮◮ – expectation is to utilize existing algorithms and ◭ ◮ software for solution. Page 3 of 12 • The “scarce resource” is increasingly in formulation, not hardware or optimization software itself. Go Back Full Screen • This book focuses on formulation of problems. Close Quit
Outline Why another . . . Problem classes Formulation of problems Case studies Algorithms Organization Level of development 3. Problem classes Software Additional materials Conclusion • Continuous variables and functions. • Incrementally defines and discusses: Home Page Title Page 1. linear systems of equations, ◭◭ ◮◮ 2. non-linear systems of equations, ◭ ◮ 3. unconstrained optimization, Page 4 of 12 4. equality-constrained optimization, Go Back 5. inequality-constrained optimization. Full Screen Close Quit
Outline 4. Formulation of problems Why another . . . Problem classes Formulation of problems • The book presents engineering applications through a Case studies series of fourteen detailed case studies. Algorithms Organization Level of development • The case studies illustrate: Software Additional materials – formulation of simultaneous equations and opti- Conclusion mization problems, – transformation of problem formulations, Home Page – solution of problems with existing general-purpose Title Page software, and ◭◭ ◮◮ – incremental development of formulations. ◭ ◮ • Simultaneous equations problems are covered in detail Page 5 of 12 since many signal processing and other engineering Go Back applications involve the solution of equations. Full Screen – Solution of optimality conditions for optimization Close problems builds directly on solution of simultane- Quit ous equations.
Outline 5. Case studies Why another . . . Problem classes Formulation of problems Case studies Analysis of a direct Discrete-time Linear Algorithms linear system equations current linear circuit Organization ◗◗◗ Level of development ❄ s ◗ Software Direct current Electric Non-linear Additional materials power system equations non-linear circuit Conclusion ✂ ✂ ❄ ✲ ✂ Multi-variate Power system Unconstrained ❇ ✂ linear regression optimization state estimation ❇ ✂ Home Page ✂ ❇ ❄ ❇ Title Page Equality- ❇ Least-cost State estimation constrained ❇ production zero injection buses ◭◭ ◮◮ ❇ optimization ❇ ❄ ❇ ◭ ◮ Production with Least absolute ❇ ❇ ◆ ✂ capacity constraints value estimation ✂ Page 6 of 12 ✂ ❄ ✂ Go Back Optimal ✂ Inequality- Pattern ✌ ✂ power flow classification constrained Full Screen optimization Close Sizing of Routing in a gate interconnects data network Quit
Outline Why another . . . Problem classes 6. Algorithms Formulation of problems Case studies Algorithms • One or two exemplar algorithms are introduced for Organization Level of development each problem class to illustrate the issues that arise Software in formulating problems. Additional materials Conclusion • Emphasize: – monotonicity, Home Page – convexity, Title Page – problem transformations, ◭◭ ◮◮ – symmetry, and ◭ ◮ – sparsity. Page 7 of 12 Go Back • Avoid details that are not prominent in problem for- mulation: Full Screen Close – variations and extensions introduced briefly. Quit
Outline Why another . . . Problem classes 7. Organization Formulation of problems Case studies Algorithms • Three introductory chapters outline the problem Organization Level of development classes and discuss problem transformations. Software Additional materials • The remaining chapters are organized in five Parts. Conclusion • Each Part deals with a problem class and consists of chapters describing: Home Page Title Page – formulation of at least two case studies, ◭◭ ◮◮ – algorithms to solve the problem class, ◭ ◮ – sensitivity analysis, and Page 8 of 12 – solution of the case studies. Go Back • Each chapter has a number of homework exercises: Full Screen – Over three hundred pages of homework solutions Close available to instructors. Quit
Outline Why another . . . Problem classes Formulation of problems Case studies Algorithms Organization Level of development Software 8. Level of development Additional materials Conclusion • Aimed at incoming graduate students or senior un- dergraduates. Home Page Title Page • Formal discussion in definition–theorem–proof style. ◭◭ ◮◮ • Complemented by: ◭ ◮ – considerable discussion, Page 9 of 12 – many worked examples, and Go Back – about 200 figures. Full Screen Close Quit
Outline Why another . . . Problem classes Formulation of problems Case studies Algorithms 9. Software Organization Level of development Software • The Matlab Optimization Toolbox is used in some Additional materials Conclusion of the homework exercises. • Other frameworks are possibly better suited to formu- Home Page lation and solution of optimization problems. Title Page • Matlab is used by many engineering students in ◭◭ ◮◮ their research: ◭ ◮ – minimizes the “start-up” costs of learning new Page 10 of 12 packages, and Go Back – enables direct incorporation of optimization formu- Full Screen lations into research projects. Close Quit
Outline Why another . . . Problem classes Formulation of problems Case studies Algorithms Organization Level of development Software Additional materials 10. Additional materials Conclusion • Available from www.cambridge.org/9780521855648 Home Page 1. Mathematical background. Title Page ◭◭ ◮◮ 2. Proofs of results. ◭ ◮ 3. Slides that I use in teaching this course. Page 11 of 12 4. Over four hundred pages of homework solutions avail- Go Back able to instructors. Full Screen Close Quit
Outline Why another . . . Problem classes Formulation of problems Case studies Algorithms Organization Level of development Software Additional materials Conclusion 11. Conclusion Home Page • New book on solving equations and continuous opti- mization. Title Page ◭◭ ◮◮ • Emphasizes formulation of problems and transforma- tions. ◭ ◮ Page 12 of 12 • For ordering information, visit the Home Page, www.cambridge.org/9780521855648 Go Back Full Screen Close Quit
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