Optimality Conditions and Duality in Nondifferentiable Robust Optimization Problems
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초록
We consider a nondifferentiable robust optimization problem, which has a maximum function of continuously differentiable functionsand support functions as its objective function,continuously differentiable functions as its constraint functions. We prove optimality conditions for the nondifferentiable robust optimization problem. We formulate a Wolfe type dual problem for the nondifferentiable robust optimization problem and prove duality theorems.
Abstract
We consider a nondifferentiable robust optimization problem, which has a maximum function of continuously differentiable functionsand support functions as its objective function,continuously differentiable functions as its constraint functions. We prove optimality conditions for the nondifferentiable robust optimization problem. We formulate a Wolfe type dual problem for the nondifferentiable robust optimization problem and prove duality theorems.
참고문헌 (11)
- D. Bertsimas, "Constructing uncertainty sets for robust linear optimization", Oper. Res, 57, pp.1483~1495 (2009)
- A. Ben-Tal, "Robust-optimization-methodology and applications", Math. Program., Ser B, 92, pp.453~480 (2002)
- A. Ben-Tal, "A selected topics in robust convex optimization", Math. Pro-gram., Ser B, 112, pp.125~158 (2008)
- D. Bertsimas, "Robust linear optimization under general norms", Oper. Res. Lett, 32, pp.510~516 (2004)
- A. Ben-Tal, "Robust optimization, Princeton Series in Applied Mathematics" (2009)
- V. Jeyakumar, "A robust von Neumann minimax theorem for zero-sum games under bounded payoff uncertainty", Oper. Res. Lett, 39, pp.109~114 (2011)
- V. Jeyakumar, "Robust duality for generalized convex programming problems under data uncertainty", Nonlinear Analysis, 75, pp.1362~1373 (2012)
- 김문희, "Robust duality for generalized invex programming problems", 대한수학회논문집, 28(2), pp.419~423 (2013), 대한수학회
- D. Kuroiwa, "On robust multiobjective optimization", Vietnam J. Math, 40, pp.305~317 (2012)
- 이규명, "On duality theorems for robust optimization problems", 충청수학회지, 26(4), pp.723~734 (2013), 충청수학회[DOI]
- A. Shapiro, "Lectures on Stochastic Programming:Modeling and Theory", SIAM, ~ (2009)