A variational inequality approach for constrained multifacility Weber problem under gauge
Jianlin Jiang Shun Zhang Su Zhang Jie Wen
Journal of Industrial & Management Optimization 2018, 14(3): 1085-1104 doi: 10.3934/jimo.2017091

The classical multifacility Weber problem (MFWP) is one of the most important models in facility location. This paper considers more general and practical case of MFWP called constrained multifacility Weber problem (CMFWP), in which the gauge is used to measure distances and locational constraints are imposed to facilities. In particular, we develop a variational inequality approach for solving it. The CMFWP is reformulated into a linear variational inequality, whose special structures lead to new projection-type methods. Global convergence of the projection-type methods is proved under mild assumptions. Some preliminary numerical results are reported which verify the effectiveness of proposed methods.

keywords: Facility location multifacility Weber problem gauge locational constraints variational inequality approach
Subspace trust-region algorithm with conic model for unconstrained optimization
Xin Zhang Jie Wen Qin Ni
Numerical Algebra, Control & Optimization 2013, 3(2): 223-234 doi: 10.3934/naco.2013.3.223
In this paper, a new subspace algorithm is proposed for unconstrained optimization. In this new algorithm, the subspace technique is used in the trust region subproblem with conic model, and the dogleg method is modified to solve this subproblem. The global convergence of this algorithm under some reasonable conditions is established. Numerical experiment shows that this algorithm may be superior to the corresponding algorithm without using subspace technique especially for large scale problems.
keywords: conic model trust region method Unconstrained optimization subspace method global convergence.

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