A Quasi-Newton Method with Wolfe Line Searches for Multiobjective Optimization

L. F. Prudente () and D. R. Souza ()
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L. F. Prudente: Universidade Federal de Goiás
D. R. Souza: Universidade Federal de Goiás

Journal of Optimization Theory and Applications, 2022, vol. 194, issue 3, No 15, 1107-1140

Abstract: Abstract We propose a BFGS method with Wolfe line searches for unconstrained multiobjective optimization problems. The algorithm is well defined even for general nonconvex problems. Global convergence and R-linear convergence to a Pareto optimal point are established for strongly convex problems. In the local convergence analysis, if the objective functions are locally strongly convex with Lipschitz continuous Hessians, the rate of convergence is Q-superlinear. In this respect, our method exactly mimics the classical BFGS method for single-criterion optimization.

Keywords: Multiobjective optimization; Pareto optimality; Quasi-Newton methods; BFGS method; Wolfe line search; 49M15; 65K05; 90C29; 90C30 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-022-02072-5

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