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== Design Optimization Problem ==
{{Main|Optimization problem}}
The formal mathematical ([[Canonical form|standard form]]) statement of the design optimization problem is <ref>{{Cite book|url=https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf|title=Convex Optimization|last=Boyd|first=Stephen|last2=Boyd|first2=Stephen P.|last3=California)|first3=Stephen (Stanford University Boyd|last4=Vandenberghe|first4=Lieven|last5=Angeles)|first5=Lieven (University of California Vandenberghe, Los|date=2004-03-08|publisher=Cambridge University Press|year=|isbn=9780521833783|___location=|pages=|language=en}}</ref>
<math>\begin{align}
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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''.
== 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]].
<references />
== See Also ==
* [https://wiki.ece.cmu.edu/ddl/index.php/Main_Page Design Decisions Wiki (DDWiki)] : Established by the Design Decisions Laboratory at Carnegie Mellon University in 2006 as a central resource for sharing information and tools to analyze and support decision-making
* [[Mathematical optimization#Optimization problems|Mathematical optimization]]
== Further Reading ==
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