Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ON DUALITY THEOREMS FOR ROBUST OPTIMIZATION PROBLEMS

  • Lee, Gue Myung (Department of Applied Mathematics Pukyong National University) ;
  • Kim, Moon Hee (School of Free Major Tongmyong University)
  • Received : 2013.06.26
  • Accepted : 2013.09.27
  • Published : 2013.11.15
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Abstract

A robust optimization problem, which has a maximum function of continuously differentiable functions as its objective function, continuously differentiable functions as its constraint functions and a geometric constraint, is considered. We prove a necessary optimality theorem and a sufficient optimality theorem for the robust optimization problem. We formulate a Wolfe type dual problem for the robust optimization problem, which has a differentiable Lagrangean function, and establish the weak duality theorem and the strong duality theorem which hold between the robust optimization problem and its Wolfe type dual problem. Moreover, saddle point theorems for the robust optimization problem are given under convexity assumptions.

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References

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