A Nonmonotone Projected Gradient Method for Multiobjective Problems on Convex Sets

doi:10.1007/s40305-022-00410-y

Journal of the Operations Research Society of China ›› 2024, Vol. 12 ›› Issue (2): 410-427.doi: 10.1007/s40305-022-00410-y

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A Nonmonotone Projected Gradient Method for Multiobjective Problems on Convex Sets

Gabrie Aníbal Carrizo¹, Nadia Soledad Fazzio², María Laura Schuverdt²

1 Department of Mathematics, National University of the South, Bahía Blanca, Argentina;
2 Department of Mathematics, University of La Plata, La Plata, Argentina

Received:2020-12-01 Revised:2022-02-23 Online:2024-06-30 Published:2024-06-12
Contact: María Laura Schuverdt, Gabrie Aníbal Carrizo, Nadia Soledad Fazzio E-mail:schuverd@mate.unlp.edu.ar;gabriel.carrizo@uns.edu.ar;nfazzio@mate.unlp.edu.ar
Supported by:
This research was partially supported by ANPCyT (Nos. PICT 2016-0921 and PICT 2019-02172), Argentina.

Abstract

Abstract: In this work we consider an extension of the classical scalar-valued projected gradient method for multiobjective problems on convex sets. As in Fazzio et al. (Optim Lett 13:1365–1379, 2019) a parameter which controls the step length is considered and an updating rule based on the spectral gradient method from the scalar case is proposed. In the present paper, we consider an extension of the traditional nonmonotone approach of Grippo et al. (SIAM J Numer Anal 23:707–716, 1986) based on the maximum of some previous function values as suggested in Mita et al. (J Glob Optim 75:539–559, 2019) for unconstrained multiobjective optimization problems. We prove the accumulation points of sequences generated by the proposed algorithm, if they exist, are stationary points of the original problem. Numerical experiments are reported.

Key words: Multiobjective optimization, Projected gradient methods, Nonmonotone line search, Global convergence

CLC Number:

Gabrie Aníbal Carrizo, Nadia Soledad Fazzio, María Laura Schuverdt. A Nonmonotone Projected Gradient Method for Multiobjective Problems on Convex Sets[J]. Journal of the Operations Research Society of China, 2024, 12(2): 410-427.

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A Nonmonotone Projected Gradient Method for Multiobjective Problems on Convex Sets

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