Optimizing over the properly efficient set of convex multi-objective optimization problems

Kahina Ghazli (), Nicolas Gillis and Mustapha Moulaï
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Kahina Ghazli: LaROMad, Faculty of Mathematics (USTHB)
Nicolas Gillis: University of Mons
Mustapha Moulaï: LaROMad, Faculty of Mathematics (USTHB)

Annals of Operations Research, 2020, vol. 295, issue 2, No 4, 575-604

Abstract: Abstract Optimizing over the efficient set of a multi-objective optimization problem is among the difficult problems in global optimization because of its nonconvexity, even in the linear case. In this paper, we consider only properly efficient solutions which are characterized through weighted sum scalarization. We propose a numerical method to tackle this problem when the objective functions and the feasible set of the multi-objective optimization problem are convex. This algorithm penalizes progressively iterates that are not properly efficient and uses a sequence of convex nonlinear subproblems that can be solved efficiently. The proposed algorithm is shown to perform well on a set of standard problems from the literature, as it allows to obtain optimal solutions in all cases.

Keywords: Multi-objective programming; Convex optimization; Properly efficient set; Penalty approach (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10479-020-03820-4

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