The proximal point method for locally Lipschitz functions in multiobjective optimization with application to the compromise problem. (English) Zbl 1388.49013
Summary: This paper studies the constrained multiobjective optimization problem of finding Pareto critical points of vector-valued functions. The proximal point method considered by H. Bonnel et al. [SIAM J. Optim. 15, No. 4, 953–970 (2005; Zbl 1093.90054)] is extended to locally Lipschitz functions in the finite dimensional multiobjective setting. To this end, a new (scalarization-free) approach for convergence analysis of the method is proposed where the first-order optimality condition of the scalarized problem is replaced by a necessary condition for weak Pareto points of a multiobjective problem. As a consequence, this has allowed us to consider the method without any assumption of convexity over the constraint sets that determine the vectorial improvement steps. This is very important for applications; for example, to extend to a dynamic setting the famous compromise problem in management sciences and game theory.
MSC:
| 49J52 | Nonsmooth analysis |
| 65K05 | Numerical mathematical programming methods |
| 90C26 | Nonconvex programming, global optimization |
| 90C29 | Multi-objective and goal programming |
| 91E99 | Mathematical psychology |
Keywords:
proximal point method; multiobjective optimization; locally Lipschitz function; Pareto critical point; compromise problem; variational rationalityCitations:
Zbl 1093.90054References:
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