An O(n 2) Active Set Algorithm for Solving Two Related Box Constrained Parametric Quadratic Programs

Recently, O(n2) active set methods have been presented for minimizing the parametric quadratic functions (1/2)x′Dx−a′x+λ|γ′x−c| and (1/2)x′Dx−a′x+(λ/2)(γ′x−c)2, respectively, subject to l≤x≤b, for all nonnegative values of the parameter λ. Here, D is a positive diagonal n×n matrix, γ and a are arbit...

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Bibliographic Details
Published inNumerical algorithms Vol. 27; no. 4; pp. 367 - 375
Main Author Gómez, Manuel A.
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.08.2001
Subjects
Algorithms
Mathematical analysis
Quadratic equations
Quadratic programming
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ISSN1017-1398
1572-9265
DOI10.1023/A:1013830414927

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Summary:Recently, O(n2) active set methods have been presented for minimizing the parametric quadratic functions (1/2)x′Dx−a′x+λ|γ′x−c| and (1/2)x′Dx−a′x+(λ/2)(γ′x−c)2, respectively, subject to l≤x≤b, for all nonnegative values of the parameter λ. Here, D is a positive diagonal n×n matrix, γ and a are arbitrary n-vectors, c is an arbitrary scalar; l and b are arbitrary n-vectors such that l≤b. In this paper, we show that each one of these algorithms may be used to simultaneously solve both parametric programs withno additional computational cost.
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ISSN:1017-1398
1572-9265
DOI:10.1023/A:1013830414927