Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem
成果类型：
Article
署名作者：
Carrizo, Gabriel A.; Lotito, Pablo A.; Maciel, Maria C.
署名单位：
National University of the South; Instituto de Investigaciones en Ingenieria Electrica (IIIE); Comision Nacional de Energia Atomica (CNEA)
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-015-0962-6
发表日期：
2016
页码：
339-369
关键词：
摘要：
A trust-region-based algorithm for the nonconvex unconstrained multiobjective optimization problem is considered. It is a generalization of the algorithm proposed by Fliege et al. (SIAM J Optim 20:602-626, 2009), for the convex problem. Similarly to the scalar case, at each iteration a subproblem is solved and the step needs to be evaluated. Therefore, the notions of decrease condition and of predicted reduction are adapted to the vectorial case. A rule to update the trust region radius is introduced. Under differentiability assumptions, the algorithm converges to points satisfying a necessary condition for Pareto points and, in the convex case, to a Pareto points satisfying necessary and sufficient conditions. Furthermore, it is proved that the algorithm displays a q-quadratic rate of convergence. The global behavior of the algorithm is shown in the numerical experience reported.
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