Inertial forward-backward methods for solving vector optimization problems. (English) Zbl 1402.90163
Summary: We propose two forward-backward proximal point type algorithms with inertial/memory effects for determining weakly efficient solutions to a vector optimization problem consisting in vector-minimizing with respect to a given closed convex pointed cone the sum of a proper cone-convex vector function with a cone-convex differentiable one, both mapping from a Hilbert space to a Banach one. Inexact versions of the algorithms, more suitable for implementation, are provided as well, while as a byproduct one can also derive a forward-backward method for solving the mentioned problem. Numerical experiments with the proposed methods are carried out in the context of solving a portfolio optimization problem.
MSC:
| 90C29 | Multi-objective and goal programming |
| 90C48 | Programming in abstract spaces |
| 90C51 | Interior-point methods |
Keywords:
vector optimization problems; inertial proximal algorithms; forward-backward algorithms; weakly efficient solutionsReferences:
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