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Semivectorial Bilevel Optimization on Riemannian Manifolds

Henri Bonnel (henri.bonnel***at***univ-nc.nc)
Leonard Todjihounde (leonardt67***at***gmail.com)
Constantin Udriste (udriste***at***mathem.pub.ro)

Abstract: In this paper we deal with the semivectorial bilevel problem in the Riemannian setting. The upper level is a scalar optimization problem to be solved by the leader, and the lower level is a multiobjective optimization problem to be solved by several followers acting in a cooperative way inside the greatest coalition and choosing among Pareto solutions with respect to a given ordering cone. For the so-called 'optimistic problem', when the followers choice among their best responses is the most favorable for the leader, we give optimality conditions. Also for the so-called 'pessimistic problem', when there is no cooperation between the leader and the followers, and the followers choice may be the worst for the leader, we present an existence result.

Keywords: Multiobjective optimization on Riemannian manifolds, bilevel optimization, semivectorial bilevel optimization problem

Category 1: Nonlinear Optimization

Citation: J Optim Theory Appl (2015) 167:464-486 DOI 10.1007/s10957-015-0789-6


Entry Submitted: 11/21/2014
Entry Accepted: 11/21/2014
Entry Last Modified: 10/18/2015

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