A smoothing scheme for optimization problems with max-min constraints
In this paper, we apply a smoothing approach to a minimization problem with a max-min constraint (i.e., a min-max-min problem). More specifically, we first rewrite the min-max-min problem as an optimization problem with several min-constraints and then approximate each min-constraint function by a s...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
American Institute of Mathematical Sciences
2007
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| Online Access: | http://aimsciences.org/journals/pdfs.jsp?paperID=2259&mode=full http://hdl.handle.net/20.500.11937/38706 |
| Summary: | In this paper, we apply a smoothing approach to a minimization problem with a max-min constraint (i.e., a min-max-min problem). More specifically, we first rewrite the min-max-min problem as an optimization problem with several min-constraints and then approximate each min-constraint function by a smooth function. As a result, the original min-max-min optimization problem can be solved by solving a sequence of smooth optimization problems. We investigate the relationship between the global optimal value and optimal solutions of the original min-max-min optimization problem and that of the approximate smooth problem. Under some conditions, we show that the limit points of the first-order (second-order) stationary points of the smooth optimization problems are first-order (second-order) stationary points of the original min-max-min optimization problem. |
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