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# election of an objective (decision criterion), expressed in terms of the design variables, which we seek to minimize or maximize;
# determination of a set of constraints, expressed in terms of the design variables, which must be satisfied by any acceptable design;
# determination of a set of values for the design variables, which minimize (or maximize) the objective, while being feasible, namely, satisfying all the constraints.<ref>{{Cite book|url=http://principlesofoptimaldesign.org/|title=Principles of Optimal Design: Modeling and Computation|last=Papalambros|first=Panos Y.|last2=Wilde|first2=Douglass J.|date=2017-01-31|publisher=Cambridge University Press|year=|isbn=9781316867457|___location=|pages=|language=en}}</ref>
The formal mathematical statement of the design optimization problem is
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\end{align}</math>
We call <math>h, g</math> the ''set'' or ''system of'' (''functional'') ''constraints'' and <math>X</math> the ''set constraint''. <ref>{{Cite book|url=https://www.cambridge.org/core/books/principles-of-optimal-design/63D7E872E7094E80ECDBCD6679199658|title=Principles of Optimal Design|last=Papalambros|first=Panos Y.|last2=Wilde|first2=Douglass J.|date=2000|publisher=Cambridge University Press|isbn=9780511626418|___location=Cambridge|language=en|doi=10.1017/CBO9780511626418}}</ref>
== Application ==
Design Optimization applies the methods of [[mathematical optimization]] to design problem formulations and it is sometimes used interchangeably with the term [[engineering optimization]]. When the objective function ''f'' is a vector rather than a scalar, the problem becomes a [[multi-objective optimization]] one. If the design optimization problem has more than one mathematical solutions the methods of [[global optimization]] are used to identified the global optimum. Practical design optimization problems are typically solved numerically and many [[optimization software]] exist in academic and commercial forms<ref>{{Cite book|url=https://books.google.com/books?hl=en&lr=&id=wy5hBwAAQBAJ&oi=fnd&pg=PR17&dq=design+optimization+with+matlab+achille+messac&ots=n9WXaRte_T&sig=DVBwayB-6W1b2YyruSz6O2fMKAM#v=onepage&q=design%20optimization%20with%20matlab%20achille%20messac&f=false|title=Optimization in Practice with MATLAB®: For Engineering Students and Professionals|last=Messac|first=Achille|date=2015-03-19|publisher=Cambridge University Press|isbn=9781316381373|language=en}}</ref>. There are several ___domain-specific applications of design optimization posing their own specific challenges in formulating and solving the resulting problems; these include, [[shape optimization]], [[wing-shape optimization]], [[topology optimization]], [[architectural design optimization]], [[Power optimization (EDA)|power optimization]].
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