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A superlinearly convergent nonmonotone quasi-Newton method for unconstrained multiobjective optimization

Mahdavi Amiri, N ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1080/10556788.2020.1737691
  3. Publisher: Taylor and Francis Ltd , 2020
  4. Abstract:
  5. We propose and analyse a nonmonotone quasi-Newton algorithm for unconstrained strongly convex multiobjective optimization. In our method, we allow for the decrease of a convex combination of recent function values. We establish the global convergence and local superlinear rate of convergence under reasonable assumptions. We implement our scheme in the context of BFGS quasi-Newton method for solving unconstrained multiobjective optimization problems. Our numerical results show that the nonmonotone quasi-Newton algorithm uses fewer function evaluations than the monotone quasi-Newton algorithm. © 2020 Informa UK Limited, trading as Taylor & Francis Group
  6. Keywords:
  7. Efficiency ; Multiobjective programming ; Nonmonotone line search algorithm ; Nonmonotone quasi-Newton method ; Computer programming ; Newton-Raphson method ; Convex combinations ; Global conver-gence ; Multi-objective optimization problem ; Nonmonotone line search ; Quasi-newton algorithm ; Quasi-Newton methods ; Rate of convergence ; Multiobjective optimization
  8. Source: Optimization Methods and Software ; Volume 35, Issue 6 , March , 2020 , Pages 1223-1247
  9. URL: https://www.tandfonline.com/doi/abs/10.1080/10556788.2020.1737691?journalCode=goms20