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For example, [[portfolio optimization]] is often conducted in terms of [[Modern portfolio theory|mean-variance analysis]]. In this context, the efficient set is a subset of the portfolios parametrized by the portfolio mean return <math>\mu_P</math> in the problem of choosing portfolio shares to minimize the portfolio's variance of return <math>\sigma_P</math> subject to a given value of <math>\mu_P</math>; see [[Mutual fund separation theorem#Portfolio separation in mean-variance analysis|Mutual fund separation theorem]] for details. Alternatively, the efficient set can be specified by choosing the portfolio shares to maximize the function <math>\mu_P - b \sigma_P </math>; the set of efficient portfolios consists of the solutions as <math>b</math> ranges from zero to infinity.
Some of the above scalarizations involve invoking the [[minimax]] principle, where always the worst of the different objectives is optimized<ref>Xu, J., Tao, Z. (2011). Rough Multiple Objective Decision Making. Vereinigtes Königreich: CRC Press., Page 67 https://
== A posteriori methods ==
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=== Mathematical programming ===
Well-known examples of mathematical programming-based a posteriori methods are the Normal Boundary Intersection (NBI),<ref name="doi10.1137/S1052623496307510">{{Cite journal | last1 = Das | first1 = I. | last2 = Dennis | first2 = J. E. | doi = 10.1137/S1052623496307510 | title = Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems | journal = SIAM Journal on Optimization | volume = 8 | issue = 3 | pages = 631 | year = 1998 | hdl = 1911/101880| s2cid = 207081991 | hdl-access = free }}</ref> Modified Normal Boundary Intersection (NBIm),<ref name="S. Motta">{{cite journal|last=S. Motta|first=Renato|author2=Afonso, Silvana M. B. |author3=Lyra, Paulo R. M. |title=A modified NBI and NC method for the solution of N-multiobjective optimization problems|journal=Structural and Multidisciplinary Optimization|date=8 January 2012|doi=10.1007/s00158-011-0729-5|volume=46|issue=2|pages=239–259|s2cid=121122414}}</ref> Normal Constraint (NC),<ref name="ReferenceA">{{cite journal|first1=A.|last1=Messac|first2=A.|author-link1=Achille Messac|last2=Ismail-Yahaya|first3=C.A.|last3=Mattson|title=The normalized normal constraint method for generating the Pareto frontier|journal=Structural and Multidisciplinary Optimization|volume=25|issue=2|pages=86–98|year=2003|doi=10.1007/s00158-002-0276-1|s2cid=58945431}}</ref><ref name="ReferenceB">{{cite journal|first1=A.|last1=Messac|first2=C. A.|last2=Mattson|title=Normal constraint method with guarantee of even representation of complete Pareto frontier|journal=AIAA Journal|volume=42|issue=10|pages=2101–2111|year=2004|doi=10.2514/1.8977|bibcode=2004AIAAJ..42.2101M}}</ref> Successive Pareto Optimization (SPO),<ref name="ReferenceC">{{cite journal|first1=Daniel|last1=Mueller-Gritschneder|first2=Helmut|last2=Graeb|first3=Ulf|last3=Schlichtmann|title=A Successive Approach to Compute the Bounded Pareto Front of Practical Multiobjective Optimization Problems|journal=SIAM Journal on Optimization|volume=20|issue=2|pages=915–934|year=2009|doi=10.1137/080729013}}</ref> and Directed Search Domain (DSD)<ref>{{Cite journal |
=== Evolutionary algorithms ===
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