Adaptive piecewise linear relaxations for enclosure computations for nonconvex multiobjective mixed-integer quadratically constrained programs

In this paper, a new method for computing an enclosure of the nondominated set of multiobjective mixed-integer quadratically constrained programs without any convexity requirements is presented. In fact, our criterion space method makes use of piecewise linear relaxations in order to bypass the nonc...

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Vydané v:	Journal of global optimization Ročník 87; číslo 1; s. 97 - 132
Hlavní autori:	Link, Moritz, Volkwein, Stefan
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York, NY Springer US 01.09.2023 Springer Nature B.V
Predmet:	Adaptive piecewise linear relaxation Approximation Box enclosure Computer Science Convexity Enclosures Energy supply networks Linear programming Mathematics Mathematics and Statistics Mixed integer Mixed-integer nonlinear programming Multiobjective optimization Network management systems Operations Research/Decision Theory Optimization Real Functions Variables Adaptive piecewise linear relaxation 65K05 Mixed-integer nonlinear programming 90C35 Multiobjective optimization Energy supply networks 90C11 90C29 Box enclosure 90C26
ISSN:	1573-2916, 0925-5001, 1573-2916
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Abstract	In this paper, a new method for computing an enclosure of the nondominated set of multiobjective mixed-integer quadratically constrained programs without any convexity requirements is presented. In fact, our criterion space method makes use of piecewise linear relaxations in order to bypass the nonconvexity of the original problem. The method chooses adaptively which level of relaxation is needed in which parts of the image space. Furthermore, it is guaranteed that after finitely many iterations, an enclosure of the nondominated set of prescribed quality is returned. We demonstrate the advantages of this approach by applying it to multiobjective energy supply network problems.
AbstractList	In this paper, a new method for computing an enclosure of the nondominated set of multiobjective mixed-integer quadratically constrained programs without any convexity requirements is presented. In fact, our criterion space method makes use of piecewise linear relaxations in order to bypass the nonconvexity of the original problem. The method chooses adaptively which level of relaxation is needed in which parts of the image space. Furthermore, it is guaranteed that after finitely many iterations, an enclosure of the nondominated set of prescribed quality is returned. We demonstrate the advantages of this approach by applying it to multiobjective energy supply network problems.
Author	Link, Moritz Volkwein, Stefan
Author_xml	– sequence: 1 givenname: Moritz surname: Link fullname: Link, Moritz – sequence: 2 givenname: Stefan surname: Volkwein fullname: Volkwein, Stefan
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CitedBy_id	crossref_primary_10_1007_s11081_025_09999_4 crossref_primary_10_1007_s10796_024_10492_z
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SubjectTerms	Adaptive piecewise linear relaxation Approximation Box enclosure Computer Science Convexity Enclosures Energy supply networks Linear programming Mathematics Mathematics and Statistics Mixed integer Mixed-integer nonlinear programming Multiobjective optimization Network management systems Operations Research/Decision Theory Optimization Real Functions Variables
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Title	Adaptive piecewise linear relaxations for enclosure computations for nonconvex multiobjective mixed-integer quadratically constrained programs
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