A smoothing scheme for optimization problems with Max-Min constraints
X. X. Huang - School of Management, Fudan University, Shanghai 200433, China (email)
Abstract: 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.
Keywords: Min-max-min problem, smooth approximation, convergence, optimality condition.
Received: August 2006; Revised: January 2007; Available Online: April 2007.
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