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Optimality Conditions in Set-Valued Optimization
2014Let X and Y be normed spaces, let S ⊆ X be a nonempty set, let C ⊂ Y be a cone inducing a partial ordering in Y, and let \(F: X \rightrightarrows Y\) be a set-valued map.
Akhtar A. Khan +2 more
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On constrained set-valued optimization
, 2007 The set-valued optimization problem minC F(x), G(x)∩(−K) = ∅, is considered, where F : Rn Rm and G : Rn Rp are set-valued functions, and C ⊂ Rm and K ⊂ Rp are closed convex cones.
IVANOV, IVAN GINCHEV, MATTEO ROCCA
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On optimality conditions for set-valued equilibrium problems
Computational and Applied Mathematics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nguyen Le Hoang Anh +2 more
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Set-valued observers and optimal disturbance rejection
IEEE Transactions on Automatic Control, 1999The guaranteed state estimation problem for a discrete-time linear time-varying system is studied. Based on an a priori model of initial conditions and exogenous signals, a set-valued observer is constructed. This observer computes the set of all states consistent with measured output data.
Jeff S. Shamma, Kuang-Yang Tu
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Theorems of the Alternative and Optimization with Set-Valued Maps
Journal of Optimization Theory and Applications, 2000The concept of generalized cone subconvexlike set-valued maps is presented and a theorem of alternative for the system of generalized inequality-equality set-valued maps is established. By applying the theorem of the alternative and other results, necessary and sufficient optimality conditions for vector optimization problems with generalized cone ...
Yang, X. M., Yang, X. Q., Chen, G. Y.
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Conic Set-Valued Maps in Vector Optimization
Set-Valued Analysis, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jiménez Guerra, Pedro +2 more
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On Optimal Set-Valued Estimators
1988Set-valued estimators are studied in a non-Bayesian as well as in a Bayesian framework. In the first case, we base on the Bochner-integral in order to introduce the notion of unbiased set-valued estimators with minimal risk.
H. Meister, O. Moeschlin
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Dubovitskii–Milyutin Approach in Set-Valued Optimization
SIAM Journal on Control and Optimization, 2008By exploring the ideas around the Dubovitskii-Milyutin approach, necessary optimality conditions are given for various optimality notions in set-valued optimization. These optimality conditions are given by using the contingent derivative and the generalized contingent epiderivative of the objective set-valued map and the set-valued maps defining the ...
George Isac, A. A. Khan
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Optimal block size for set-valued attributes
Information Processing Letters, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Suchen H. Hsu, Richard T. Snodgrass
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On Optimization Problems with Set-Valued Objective Maps: Existence and Optimality
Journal of Optimization Theory and Applications, 2011Constrained optimization problems with set-valued objective maps are considered. Three types of quasi-ordering on the set of all non-empty subsets of the \(n\)-dimensional Euclidian space are introduced. Applying those orderings, three lower semi-continuous set valued maps are defined. The properties of lower continuity are investigated. Then, extended
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