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336
Minimax Programs
 University of California Press
, 1997
"... We introduce an optimization problem called a minimax program that is similar to a linear program, except that the addition operator is replaced in the constraint equations by the maximum operator. We clarify the relation of this problem to some betterknown problems. We identify an interesting spec ..."
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Cited by 482 (5 self)
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We introduce an optimization problem called a minimax program that is similar to a linear program, except that the addition operator is replaced in the constraint equations by the maximum operator. We clarify the relation of this problem to some betterknown problems. We identify an interesting
Minimax Programs, Bitonic Columns and PQ Trees
, 1998
"... imax program formulation. In section 3 we describe its relation to known problems. In section 4 we define a special case in which optimal solutions can be obtained efficiently, and in section 5 we give an algorithm that does so. Finally, in section 6 we briefly describe a new extension of the PQ tre ..."
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tree algorithm for efficient recognition of the special case, which may enable fast solution of other optimization problems. Due to length limitations, details and proofs are omitted here, but available in [9]. 2 A Minimax Program Consider a linear program; implicit in the definition is an assumption
HigherOrder Duality in Nondifferentiable Minimax Programming with Generalized Type I Functions
, 2008
"... Abstract A unified higherorder dual for a nondifferentiable minimax programming problem is formulated. Weak, strong and strict converse duality theorems are discussed involving generalized higherorder (F,α,ρ, d)Type I functions. ..."
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Cited by 2 (0 self)
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Abstract A unified higherorder dual for a nondifferentiable minimax programming problem is formulated. Weak, strong and strict converse duality theorems are discussed involving generalized higherorder (F,α,ρ, d)Type I functions.
Nondifferentiable Minimax Programming Problems in Complex Spaces Involving Generalized Convex Functions
"... We start our discussion with a class of nondifferentiable minimax programming problems in complex space and establish sufficient optimality conditions under generalized convexity assumptions. Furthermore, we derive weak, strong, and strict converse duality theorems for the two types of dual models ..."
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We start our discussion with a class of nondifferentiable minimax programming problems in complex space and establish sufficient optimality conditions under generalized convexity assumptions. Furthermore, we derive weak, strong, and strict converse duality theorems for the two types of dual models
On Nonsmooth SemiInfinite Minimax Programming Problem with (Φ, )Invexity
"... We are interested in a nonsmooth minimax programming Problem (SIP). Firstly, we establish the necessary optimality conditions theorems for Problem (SIP) when using the wellknown Caratheodory's theorem. Under the Lipschitz (Φ, )invexity assumptions, we derive the sufficiency of the necessary ..."
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We are interested in a nonsmooth minimax programming Problem (SIP). Firstly, we establish the necessary optimality conditions theorems for Problem (SIP) when using the wellknown Caratheodory's theorem. Under the Lipschitz (Φ, )invexity assumptions, we derive the sufficiency of the necessary
Uncertainties in minimax stochastic programs
"... When using the minimax approach one tries to hedge against the worst possible distribution belonging to a specified class P. A suitable stability analysis of results with respect to the choice of this class is an important issue. It has to be tailored to the type of the minimax problem, to the consi ..."
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When using the minimax approach one tries to hedge against the worst possible distribution belonging to a specified class P. A suitable stability analysis of results with respect to the choice of this class is an important issue. It has to be tailored to the type of the minimax problem
Minimax differential dynamic programming: An application to robust bipedwalking
 in Advances in Neural Information Processing Systems 14
, 2002
"... We have developed a robust control policy design method for highdimensional state spaces by using differential dynamic programming with a minimax criterion. As an example, we applied our method to a simulated five link biped robot. The results show lower joint torques using the optimal control poli ..."
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Cited by 70 (11 self)
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We have developed a robust control policy design method for highdimensional state spaces by using differential dynamic programming with a minimax criterion. As an example, we applied our method to a simulated five link biped robot. The results show lower joint torques using the optimal control
On a class of minimax stochastic programs
 SIAM J. Optim
, 2004
"... Abstract. For a particular class of minimax stochastic programming models, we show that the problem can be equivalently reformulated into a standard stochastic programming problem. This permits the direct use of standard decomposition and sampling methods developed for stochastic programming. We als ..."
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Cited by 23 (3 self)
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Abstract. For a particular class of minimax stochastic programming models, we show that the problem can be equivalently reformulated into a standard stochastic programming problem. This permits the direct use of standard decomposition and sampling methods developed for stochastic programming. We
Results 1  10
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336