Minimal Pairs of Convex Sets

Pallaschke, Diethard; Urbański, Ryszard

doi:10.1007/978-94-015-9920-7_4

Cited by 10 publications

(15 citation statements)

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“…This property was first given by Pallaschke and Urbanski [11] for compact convex sets in topological vector spaces which is an useful property in investigating pairs of compact convex sets in topological vector spaces [12,13]. whereas the converse implications do not hold in general as shown in the following simple example.…”

Section: Preliminariesmentioning

confidence: 87%

(F, K, b)-vex sets and some related properties

Zang

Liu

2013

International Journal of Computer Mathematics

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Section: Preliminariesmentioning

confidence: 87%

(F, K, b)-vex sets and some related properties

Zang

Liu

2013

International Journal of Computer Mathematics

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“…(Note that this intersection is not empty, since [p 0 , q 0 ] ⊂ A ∩ B ⊂ (A F ) ∪ (B F ).) Notice that by (ii) or (iii) and [6], Proposition 2.5(iii)…”

Section: Proposition 3 Let X Be a Topological Vector Space And Letmentioning

confidence: 88%

On inclusion and summands of bounded closed convex sets

Grzybowski

Urbański

2005

Acta Math Hung

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“…As we know, the uppersemicontinuity of the quasidifferential is required in many existing algorithms of quasidifferentiable optimization [3] and of quasidifferentiable equations [16]. Many publications dealt with this problem, see for instance [8,9,11,14,15,17].…”

Section: Yan Gaomentioning

confidence: 99%

Representative of Quasidifferentials and Its Formula for a Quasidifferentiable Function

Gao

2005

Set-Valued Anal

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The quasidifferential of a quasidifferentiable function in the sense of Demyanov and Rubinov is not uniquely defined. Xia proposed the notion of the kernelled quasidifferential, which is expected to be a representative for the equivalent class of quasidifferentials. In the 2-dimensional case, the existence of the kernelled quasidifferential was shown. In this paper, the existence of the kernelled quasidifferential in the n-dimensional space (n > 2) is proved under the assumption that the Minkowski difference and the Demyanov difference of subdifferential and minus superdifferential coincide. In particular, given a quasidifferential, the kernelled quasidifferential can be formulated. Applications to two classes of generalized separable quasidifferentiable functions are developed. (2000): 49J52, 54C60, 90C26. Mathematics Subject Classifications

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Minimal Pairs of Convex Sets

Cited by 10 publications

References 0 publications

(F, K, b)-vex sets and some related properties

(F, K, b)-vex sets and some related properties

On inclusion and summands of bounded closed convex sets

Representative of Quasidifferentials and Its Formula for a Quasidifferentiable Function

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