Ascent and descent cones of ordered median block functions

J. Grzybowski; J. Kalcsics; S. Nickel; D. Pallaschke; R. Urbański

doi:10.1080/02331934.2018.1429432

Ascent and descent cones of ordered median block functions

J. Grzybowski, J. Kalcsics, S. Nickel, D. Pallaschke^*, R. Urbański

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study properties of a special class of ordered median functions, called block-functions. These are ordered median functions which belong to a generating binary (row)-vector of the form λ = (0, 0, . . , 0, 1, 1, . . , 1, 0, 0, . . , 0) ∈ Rⁿ, called a block vector. The aim of this paper is to explicitly determine the simplicial complexes and all steepest descent and ascent directions of descent and ascent cones of ordered median block-function.

Original language	English
Pages (from-to)	507-522
Number of pages	16
Journal	Optimization
Volume	67
Issue number	5
DOIs	https://doi.org/10.1080/02331934.2018.1429432
Publication status	Published - 25 Jan 2018

Keywords / Materials (for Non-textual outputs)

ascent- and descent directions
convex analysis
Ordered median functions

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10.1080/02331934.2018.1429432

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title = "Ascent and descent cones of ordered median block functions",

abstract = "In this paper, we study properties of a special class of ordered median functions, called block-functions. These are ordered median functions which belong to a generating binary (row)-vector of the form λ = (0, 0, . . , 0, 1, 1, . . , 1, 0, 0, . . , 0) ∈ Rn, called a block vector. The aim of this paper is to explicitly determine the simplicial complexes and all steepest descent and ascent directions of descent and ascent cones of ordered median block-function.",

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author = "J. Grzybowski and J. Kalcsics and S. Nickel and D. Pallaschke and R. Urba{\'n}ski",

note = "Publisher Copyright: {\textcopyright} 2018 Informa UK Limited, trading as Taylor \& Francis Group.",

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T1 - Ascent and descent cones of ordered median block functions

AU - Grzybowski, J.

AU - Kalcsics, J.

AU - Nickel, S.

AU - Pallaschke, D.

AU - Urbański, R.

PY - 2018/1/25

Y1 - 2018/1/25

N2 - In this paper, we study properties of a special class of ordered median functions, called block-functions. These are ordered median functions which belong to a generating binary (row)-vector of the form λ = (0, 0, . . , 0, 1, 1, . . , 1, 0, 0, . . , 0) ∈ Rn, called a block vector. The aim of this paper is to explicitly determine the simplicial complexes and all steepest descent and ascent directions of descent and ascent cones of ordered median block-function.

AB - In this paper, we study properties of a special class of ordered median functions, called block-functions. These are ordered median functions which belong to a generating binary (row)-vector of the form λ = (0, 0, . . , 0, 1, 1, . . , 1, 0, 0, . . , 0) ∈ Rn, called a block vector. The aim of this paper is to explicitly determine the simplicial complexes and all steepest descent and ascent directions of descent and ascent cones of ordered median block-function.

KW - ascent- and descent directions

KW - convex analysis

KW - Ordered median functions

U2 - 10.1080/02331934.2018.1429432

DO - 10.1080/02331934.2018.1429432

M3 - Article

AN - SCOPUS:85040976111

SN - 0233-1934

VL - 67

SP - 507

EP - 522

JO - Optimization

JF - Optimization

IS - 5

ER -

Ascent and descent cones of ordered median block functions

Abstract

Keywords / Materials (for Non-textual outputs)

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