Abstract
Duality and penalty methods are popular in optimization. The study on duality and penalty methods for nonconvex multiobjective optimization problems is very limited. In this paper, we introduce vector-valued nonlinear Lagrangian and penalty functions and formulate nonlinear Lagrangian dual problems and nonlinear penalty problems for multiobjective constrained optimization problems. We establish strong duality and exact penalization results. The strong duality is an inclusion between the set of infimum points of the original multiobjective constrained optimization problem and that of the nonlinear Lagrangian dual problem. Exact penalization is established via a generalized calmness-type condition.
Original language | English |
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Pages (from-to) | 675-692 |
Number of pages | 18 |
Journal | SIAM Journal on Optimization |
Volume | 13 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Jan 2003 |
Keywords
- Duality
- Exact penalization
- Multiobjective optimization
- Nonlinear Lagrangian function
- Stability
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics