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7Pineda-Villavicencio, Guillermo
5Ugon, Julien
3Yost, David
2Gfrerer, Helmut
2Kruger, Alexander
2López, Marco
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2Outrata, Jiri
2Théra, Michel
1Abbasi, Malek
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1Bui, Hoa
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124901 Applied mathematics
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On the application of the SCD semismooth* newton method to variational inequalities of the second kind

- Gfrerer, Helmut, Outrata, Jiri, Valdman, Jan

**Authors:**Gfrerer, Helmut , Outrata, Jiri , Valdman, Jan**Date:**2022**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 30, no. 4 (2022), p. 1453-1484**Relation:**https://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**The paper starts with a description of SCD (subspace containing derivative) mappings and the SCD Newton method for the solution of general inclusions. This method is then applied to a class of variational inequalities of the second kind. As a result, one obtains an implementable algorithm which exhibits locally superlinear convergence. Thereafter we suggest several globally convergent hybrid algorithms in which one combines the SCD Newton method with selected splitting algorithms for the solution of monotone variational inequalities. Finally, we demonstrate the efficiency of one of these methods via a Cournot-Nash equilibrium, modeled as a variational inequality of the second kind, where one admits really large numbers of players (firms) and produced commodities. © 2022, The Author(s), under exclusive licence to Springer Nature B.V.

**Authors:**Gfrerer, Helmut , Outrata, Jiri , Valdman, Jan**Date:**2022**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 30, no. 4 (2022), p. 1453-1484**Relation:**https://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**The paper starts with a description of SCD (subspace containing derivative) mappings and the SCD Newton method for the solution of general inclusions. This method is then applied to a class of variational inequalities of the second kind. As a result, one obtains an implementable algorithm which exhibits locally superlinear convergence. Thereafter we suggest several globally convergent hybrid algorithms in which one combines the SCD Newton method with selected splitting algorithms for the solution of monotone variational inequalities. Finally, we demonstrate the efficiency of one of these methods via a Cournot-Nash equilibrium, modeled as a variational inequality of the second kind, where one admits really large numbers of players (firms) and produced commodities. © 2022, The Author(s), under exclusive licence to Springer Nature B.V.

Isolated calmness and sharp minima via Hölder Graphical Derivatives

- Kruger, Alexander, López, Marco, Yang, Xiaoqi, Zhu, Jiangxing

**Authors:**Kruger, Alexander , López, Marco , Yang, Xiaoqi , Zhu, Jiangxing**Date:**2022**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 30, no. 4 (2022), p. 1423-1441**Relation:**https://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**The paper utilizes Hölder graphical derivatives for characterizing Hölder strong subregularity, isolated calmness and sharp minimum. As applications, we characterize Hölder isolated calmness in linear semi-infinite optimization and Hölder sharp minimizers of some penalty functions for constrained optimization. © 2022, The Author(s).

**Authors:**Kruger, Alexander , López, Marco , Yang, Xiaoqi , Zhu, Jiangxing**Date:**2022**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 30, no. 4 (2022), p. 1423-1441**Relation:**https://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**The paper utilizes Hölder graphical derivatives for characterizing Hölder strong subregularity, isolated calmness and sharp minimum. As applications, we characterize Hölder isolated calmness in linear semi-infinite optimization and Hölder sharp minimizers of some penalty functions for constrained optimization. © 2022, The Author(s).

Karl Heinrich Hofmann and the structure of compact groups and pro-lie groups

**Authors:**Morris, Sidney**Date:**2023**Type:**Text , Journal article**Relation:**Journal of Lie Theory Vol. 33, no. 1 (2023), p. 5-28**Full Text:**false**Reviewed:****Description:**This article is dedicated to Karl Heinrich Hofmann on his 90th birthday. The first part of the article records some biographical facts about him. The second part focuses on the research papers and books he published with the author of this article over the last 45 years. These results concern the structure of compact groups and pro-Lie groups. © 2023 Heldermann Verlag.

On the isolated calmness property of implicitly defined multifunctions

- Gfrerer, Helmut, Outrata, Jiri

**Authors:**Gfrerer, Helmut , Outrata, Jiri**Date:**2023**Type:**Text , Journal article**Relation:**Journal of Convex Analysis Vol. 30, no. 3 (2023), p. 1001-1023**Relation:**https://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**The paper deals with an extension of the available theory of SCD (subspace containing derivatives) mappings to mappings between spaces of different dimensions. This extension enables us to derive workable sufficient conditions for the isolated calmness of implicitly defined multifunctions around given reference points. This stability property differs substantially from isolated calmness at a point and, possibly in conjunction with the Aubin property, offers a new useful stability concept. The application area includes a broad class of parameterized generalized equations, where the respective conditions ensure a rather strong type of Lipschitzian behavior of their solution maps. © 2023 Heldermann Verlag. All rights reserved.

**Authors:**Gfrerer, Helmut , Outrata, Jiri**Date:**2023**Type:**Text , Journal article**Relation:**Journal of Convex Analysis Vol. 30, no. 3 (2023), p. 1001-1023**Relation:**https://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**The paper deals with an extension of the available theory of SCD (subspace containing derivatives) mappings to mappings between spaces of different dimensions. This extension enables us to derive workable sufficient conditions for the isolated calmness of implicitly defined multifunctions around given reference points. This stability property differs substantially from isolated calmness at a point and, possibly in conjunction with the Aubin property, offers a new useful stability concept. The application area includes a broad class of parameterized generalized equations, where the respective conditions ensure a rather strong type of Lipschitzian behavior of their solution maps. © 2023 Heldermann Verlag. All rights reserved.

Linkedness of cartesian products of complete graphs

- Jorgensen, Leif, Pineda-Villavicencio, Guillermo, Ugon, Julien

**Authors:**Jorgensen, Leif , Pineda-Villavicencio, Guillermo , Ugon, Julien**Date:**2022**Type:**Text , Journal article**Relation:**Ars Mathematica Contemporanea Vol. 22, no. 2 (2022), p.**Relation:**http://purl.org/au-research/grants/arc/DP180100602**Full Text:****Reviewed:****Description:**This paper is concerned with the linkedness of Cartesian products of complete graphs. A graph with at least 2k vertices is k-linked if, for every set of 2k distinct vertices organised in arbitrary k pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We show that the Cartesian product Kd1+1 × Kd2+1 of complete graphs Kd1+1 and Kd2+1 is

**Authors:**Jorgensen, Leif , Pineda-Villavicencio, Guillermo , Ugon, Julien**Date:**2022**Type:**Text , Journal article**Relation:**Ars Mathematica Contemporanea Vol. 22, no. 2 (2022), p.**Relation:**http://purl.org/au-research/grants/arc/DP180100602**Full Text:****Reviewed:****Description:**This paper is concerned with the linkedness of Cartesian products of complete graphs. A graph with at least 2k vertices is k-linked if, for every set of 2k distinct vertices organised in arbitrary k pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We show that the Cartesian product Kd1+1 × Kd2+1 of complete graphs Kd1+1 and Kd2+1 is

The linkedness of cubical polytopes : beyond the cube

- Bui, Hoa, Pineda-Villavicencio, Guillermo, Ugon, Julien

**Authors:**Bui, Hoa , Pineda-Villavicencio, Guillermo , Ugon, Julien**Date:**2024**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 347, no. 3 (2024), p.**Relation:**https://purl.org/au-research/grants/arc/DP180100602**Full Text:****Reviewed:****Description:**A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least 2k vertices is k-linked if, for every set of k disjoint pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We say that a polytope is k-linked if its graph is k-linked. In a previous paper [3] we proved that every cubical d-polytope is ⌊d/2⌋-linked. Here we strengthen this result by establishing the ⌊(d+1)/2⌋-linkedness of cubical d-polytopes, for every d≠3. A graph G is strongly k-linked if it has at least 2k+1 vertices and, for every vertex v of G, the subgraph G−v is k-linked. We say that a polytope is (strongly) k-linked if its graph is (strongly) k-linked. In this paper, we also prove that every cubical d-polytope is strongly ⌊d/2⌋-linked, for every d≠3. These results are best possible for this class of polytopes.**Description:**A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least 2k vertices is k-linked if, for every set of k disjoint pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We say that a polytope is k-linked if its graph is k-linked. In a previous paper [3] we proved that every cubical d-polytope is

**Authors:**Bui, Hoa , Pineda-Villavicencio, Guillermo , Ugon, Julien**Date:**2024**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 347, no. 3 (2024), p.**Relation:**https://purl.org/au-research/grants/arc/DP180100602**Full Text:****Reviewed:****Description:**A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least 2k vertices is k-linked if, for every set of k disjoint pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We say that a polytope is k-linked if its graph is k-linked. In a previous paper [3] we proved that every cubical d-polytope is ⌊d/2⌋-linked. Here we strengthen this result by establishing the ⌊(d+1)/2⌋-linkedness of cubical d-polytopes, for every d≠3. A graph G is strongly k-linked if it has at least 2k+1 vertices and, for every vertex v of G, the subgraph G−v is k-linked. We say that a polytope is (strongly) k-linked if its graph is (strongly) k-linked. In this paper, we also prove that every cubical d-polytope is strongly ⌊d/2⌋-linked, for every d≠3. These results are best possible for this class of polytopes.**Description:**A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least 2k vertices is k-linked if, for every set of k disjoint pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We say that a polytope is k-linked if its graph is k-linked. In a previous paper [3] we proved that every cubical d-polytope is

The lower bound theorem for d - polytopes with 2d + 1 vertices

- Pineda-Villavicencio, Guillermo, Yost, David

**Authors:**Pineda-Villavicencio, Guillermo , Yost, David**Date:**2022**Type:**Text , Journal article**Relation:**SIAM Journal on Discrete Mathematics Vol. 36, no. 4 (2022), p. 2920-2941**Full Text:****Reviewed:****Description:**The problem of calculating exact lower bounds for the number of k-faces of dpolytopes with n vertices, for each value of k, and characterizing the minimizers has recently been solved for n not exceeding 2d. We establish the corresponding result for n = 2d+ 1; the nature of the lower bounds and the minimizing polytopes are quite different in this case. As a byproduct, we also characterize all d-polytopes with d + 3 vertices and only one or two edges more than the minimum. © 2022 Society for Industrial and Applied Mathematics.

**Authors:**Pineda-Villavicencio, Guillermo , Yost, David**Date:**2022**Type:**Text , Journal article**Relation:**SIAM Journal on Discrete Mathematics Vol. 36, no. 4 (2022), p. 2920-2941**Full Text:****Reviewed:****Description:**The problem of calculating exact lower bounds for the number of k-faces of dpolytopes with n vertices, for each value of k, and characterizing the minimizers has recently been solved for n not exceeding 2d. We establish the corresponding result for n = 2d+ 1; the nature of the lower bounds and the minimizing polytopes are quite different in this case. As a byproduct, we also characterize all d-polytopes with d + 3 vertices and only one or two edges more than the minimum. © 2022 Society for Industrial and Applied Mathematics.

Virtual care initiatives for older adults in Australia : scoping review

- Savira, Feby, Gupta, Adyya, Gilbert, Cecily, Huggins, Catherine, Browning, Colette, Chapman, Wendy, Haines, Terry, Peeters, Anna

**Authors:**Savira, Feby , Gupta, Adyya , Gilbert, Cecily , Huggins, Catherine , Browning, Colette , Chapman, Wendy , Haines, Terry , Peeters, Anna**Date:**2023**Type:**Text , Journal article , Review**Relation:**Journal of Medical Internet Research Vol. 25, no. (2023), p.**Full Text:****Reviewed:****Description:**Background: There has been a rapid shift toward the adoption of virtual health care services in Australia. It is unknown how widely virtual care has been implemented or evaluated for the care of older adults in Australia. Objective: We aimed to review the literature evaluating virtual care initiatives for older adults across a wide range of health conditions and modalities and identify key challenges and opportunities for wider adoption at both patient and system levels in Australia. Methods: A scoping review of the literature was conducted. We searched MEDLINE, Embase, PsycINFO, CINAHL, AgeLine, and gray literature (January 1, 2011, to March 8, 2021) to identify virtual care initiatives for older Australians (aged

**Authors:**Savira, Feby , Gupta, Adyya , Gilbert, Cecily , Huggins, Catherine , Browning, Colette , Chapman, Wendy , Haines, Terry , Peeters, Anna**Date:**2023**Type:**Text , Journal article , Review**Relation:**Journal of Medical Internet Research Vol. 25, no. (2023), p.**Full Text:****Reviewed:****Description:**Background: There has been a rapid shift toward the adoption of virtual health care services in Australia. It is unknown how widely virtual care has been implemented or evaluated for the care of older adults in Australia. Objective: We aimed to review the literature evaluating virtual care initiatives for older adults across a wide range of health conditions and modalities and identify key challenges and opportunities for wider adoption at both patient and system levels in Australia. Methods: A scoping review of the literature was conducted. We searched MEDLINE, Embase, PsycINFO, CINAHL, AgeLine, and gray literature (January 1, 2011, to March 8, 2021) to identify virtual care initiatives for older Australians (aged

Transcendental groups

**Authors:**Morris, Sidney**Date:**2024**Type:**Text , Journal article**Relation:**Topology Proceedings Vol. 63, no. (2024), p. 167-176**Full Text:****Reviewed:****Description:**In this note we introduce the notion of a transcendental group, that is, a subgroup G of the topological group C of all complex numbers such that every element of G except 0 is a transcendental number. All such topological groups are separable metrizable torsion-free abelian groups. If G

**Authors:**Morris, Sidney**Date:**2024**Type:**Text , Journal article**Relation:**Topology Proceedings Vol. 63, no. (2024), p. 167-176**Full Text:****Reviewed:****Description:**In this note we introduce the notion of a transcendental group, that is, a subgroup G of the topological group C of all complex numbers such that every element of G except 0 is a transcendental number. All such topological groups are separable metrizable torsion-free abelian groups. If G

Primal Characterizations of error bounds for composite-convex inequalities

- Wei, Zhou, Théra, Michel, Yao, Jen-Chih

**Authors:**Wei, Zhou , Théra, Michel , Yao, Jen-Chih**Date:**2023**Type:**Text , Journal article**Relation:**Journal of Convex Analysis Vol. 30, no. 4 (2023), p. 1329-1350**Full Text:****Reviewed:****Description:**This paper is devoted to primal conditions of error bounds for a general function. In terms of Bouligand tangent cones, lower Hadamard directional derivatives and the Hausdorff-Pompeiu excess of subsets, we provide several necessary and/or sufficient conditions for error bounds with mild assumptions. Then we use these primal results to characterize error bounds for composite-convex functions (i.e. the composition of a convex function with a continuously differentiable mapping). It is proved that the primal characterization of error bounds can be established via Bouligand tangent cones, directional derivatives and the Hausdorff-Pompeiu excess if the mapping is metrically regular at the given point. The accurate estimate on the error bound modulus is also obtained. © 2023 Heldermann Verlag. All rights reserved.

**Authors:**Wei, Zhou , Théra, Michel , Yao, Jen-Chih**Date:**2023**Type:**Text , Journal article**Relation:**Journal of Convex Analysis Vol. 30, no. 4 (2023), p. 1329-1350**Full Text:****Reviewed:****Description:**This paper is devoted to primal conditions of error bounds for a general function. In terms of Bouligand tangent cones, lower Hadamard directional derivatives and the Hausdorff-Pompeiu excess of subsets, we provide several necessary and/or sufficient conditions for error bounds with mild assumptions. Then we use these primal results to characterize error bounds for composite-convex functions (i.e. the composition of a convex function with a continuously differentiable mapping). It is proved that the primal characterization of error bounds can be established via Bouligand tangent cones, directional derivatives and the Hausdorff-Pompeiu excess if the mapping is metrically regular at the given point. The accurate estimate on the error bound modulus is also obtained. © 2023 Heldermann Verlag. All rights reserved.

Fuzzy multiplier, sum and intersection rules in non-Lipschitzian settings : decoupling approach revisited

- Fabian, Marian, Kruger, Alexander, Mehlitz, Patrick

**Authors:**Fabian, Marian , Kruger, Alexander , Mehlitz, Patrick**Date:**2024**Type:**Text , Journal article**Relation:**Journal of Mathematical Analysis and Applications Vol. 532, no. 2 (2024), p.**Relation:**https://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**We revisit the decoupling approach widely used (often intuitively) in nonlinear analysis and optimization and initially formalized about a quarter of a century ago by Borwein & Zhu, Borwein & Ioffe and Lassonde. It allows one to streamline proofs of necessary optimality conditions and calculus relations, unify and simplify the respective statements, clarify and in many cases weaken the assumptions. In this paper we study weaker concepts of quasiuniform infimum, quasiuniform lower semicontinuity and quasiuniform minimum, putting them into the context of the general theory developed by the aforementioned authors. Along the way, we unify the terminology and notation and fill in some gaps in the general theory. We establish rather general primal and dual necessary conditions characterizing quasiuniform

**Authors:**Fabian, Marian , Kruger, Alexander , Mehlitz, Patrick**Date:**2024**Type:**Text , Journal article**Relation:**Journal of Mathematical Analysis and Applications Vol. 532, no. 2 (2024), p.**Relation:**https://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**We revisit the decoupling approach widely used (often intuitively) in nonlinear analysis and optimization and initially formalized about a quarter of a century ago by Borwein & Zhu, Borwein & Ioffe and Lassonde. It allows one to streamline proofs of necessary optimality conditions and calculus relations, unify and simplify the respective statements, clarify and in many cases weaken the assumptions. In this paper we study weaker concepts of quasiuniform infimum, quasiuniform lower semicontinuity and quasiuniform minimum, putting them into the context of the general theory developed by the aforementioned authors. Along the way, we unify the terminology and notation and fill in some gaps in the general theory. We establish rather general primal and dual necessary conditions characterizing quasiuniform

Minimum number of edges of polytopes with 2d + 2 vertices

- Pineda-Villavicencio, Guillermo, Ugon, Julien, Yost, David

**Authors:**Pineda-Villavicencio, Guillermo , Ugon, Julien , Yost, David**Date:**2022**Type:**Text , Journal article**Relation:**Electronic Journal of Combinatorics Vol. 29, no. 3 (2022), p.**Relation:**http://purl.org/au-research/grants/arc/DP180100602**Full Text:****Reviewed:****Description:**We define two d-polytopes, both with 2d + 2 vertices and (d + 3)(d

**Authors:**Pineda-Villavicencio, Guillermo , Ugon, Julien , Yost, David**Date:**2022**Type:**Text , Journal article**Relation:**Electronic Journal of Combinatorics Vol. 29, no. 3 (2022), p.**Relation:**http://purl.org/au-research/grants/arc/DP180100602**Full Text:****Reviewed:****Description:**We define two d-polytopes, both with 2d + 2 vertices and (d + 3)(d

Reconstructibility of matroid polytopes

- Pineda-Villavicencio, Guillermo, Schroter, Benjamin

**Authors:**Pineda-Villavicencio, Guillermo , Schroter, Benjamin**Date:**2022**Type:**Text , Journal article**Relation:**SIAM Journal on Discrete Mathematics Vol. 36, no. 1 (2022), p. 490-508**Full Text:****Reviewed:****Description:**We specify what is meant for a polytope to be reconstructible from its graph or dual graph, and we introduce the problem of class reconstructibility; i.e., the face lattice of the polytope can be determined from the (dual) graph within a given class. We provide examples of cubical polytopes that are not reconstructible from their dual graphs. Furthermore, we show that matroid (base) polytopes are not reconstructible from their graphs and not class reconstructible from their dual graphs; our counterexamples include hypersimplices. Additionally, we prove that matroid polytopes are class reconstructible from their graphs, and we present an O(n3) algorithm that computes the vertices of a matroid polytope from its n-vertex graph. Moreover, our proof includes a characterization of all matroids with isomorphic basis exchange graphs. © 2022 Society for Industrial and Applied Mathematics

**Authors:**Pineda-Villavicencio, Guillermo , Schroter, Benjamin**Date:**2022**Type:**Text , Journal article**Relation:**SIAM Journal on Discrete Mathematics Vol. 36, no. 1 (2022), p. 490-508**Full Text:****Reviewed:****Description:**We specify what is meant for a polytope to be reconstructible from its graph or dual graph, and we introduce the problem of class reconstructibility; i.e., the face lattice of the polytope can be determined from the (dual) graph within a given class. We provide examples of cubical polytopes that are not reconstructible from their dual graphs. Furthermore, we show that matroid (base) polytopes are not reconstructible from their graphs and not class reconstructible from their dual graphs; our counterexamples include hypersimplices. Additionally, we prove that matroid polytopes are class reconstructible from their graphs, and we present an O(n3) algorithm that computes the vertices of a matroid polytope from its n-vertex graph. Moreover, our proof includes a characterization of all matroids with isomorphic basis exchange graphs. © 2022 Society for Industrial and Applied Mathematics

Minimum number of edges of polytopes with $2d+2$ Vertices

- Pineda-Villavicencio, Guillermo, Ugon, Julien, Yost, David

**Authors:**Pineda-Villavicencio, Guillermo , Ugon, Julien , Yost, David**Date:**2022**Type:**Text , Journal article**Relation:**The Electronic journal of combinatorics Vol. 29, no. 3 (2022), p.**Full Text:****Reviewed:****Description:**We define two $d$-polytopes, both with $2d+2$ vertices and $(d+3)(d-1)$ edges, which reduce to the cube and the 5-wedge in dimension three. We show that they are the only minimisers of the number of edges, amongst all $d$-polytopes with $2d+2$ vertices, when $d=6$ or $d\ge8$. We also characterise the minimising polytopes for $d=4, 5$ or 7, where four sporadic examples arise.

**Authors:**Pineda-Villavicencio, Guillermo , Ugon, Julien , Yost, David**Date:**2022**Type:**Text , Journal article**Relation:**The Electronic journal of combinatorics Vol. 29, no. 3 (2022), p.**Full Text:****Reviewed:****Description:**We define two $d$-polytopes, both with $2d+2$ vertices and $(d+3)(d-1)$ edges, which reduce to the cube and the 5-wedge in dimension three. We show that they are the only minimisers of the number of edges, amongst all $d$-polytopes with $2d+2$ vertices, when $d=6$ or $d\ge8$. We also characterise the minimising polytopes for $d=4, 5$ or 7, where four sporadic examples arise.

Edge connectivity of simplicial polytopes

- Pilaud, Vincent, Pineda-Villavicencio, Guillermo, Ugon, Julien

**Authors:**Pilaud, Vincent , Pineda-Villavicencio, Guillermo , Ugon, Julien**Date:**2023**Type:**Text , Journal article**Relation:**European Journal of Combinatorics Vol. 113, no. (2023), p.**Relation:**https://purl.org/au-research/grants/arc/DP180100602**Full Text:**false**Reviewed:****Description:**We show that the graph of a simplicial polytope of dimension d ≥ 3 has no nontrivial minimum edge cut with fewer than d(d+1)/2 edges, hence the graph is min{δ,d(d+1)/2}-edgeconnected where δ denotes the minimum degree. When d = 3, this implies that every minimum edge cut in a plane triangulation is trivial. When d ≥ 4, we construct a simplicial d-polytope whose graph has a nontrivial minimum edge cut of cardinality d(d + 1)/2, proving that the aforementioned result is best possible.**Description:**We show that the graph of a simplicial polytope of dimension d

Conjugation-based approach to the ε-subdifferential of convex suprema

- Correa, Rafael, Hantoute, Abderrahim, López, Marco

**Authors:**Correa, Rafael , Hantoute, Abderrahim , López, Marco**Date:**2024**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 32, no. 1 (2024), p.**Full Text:****Reviewed:****Description:**We provide new characterizations of the

**Authors:**Correa, Rafael , Hantoute, Abderrahim , López, Marco**Date:**2024**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 32, no. 1 (2024), p.**Full Text:****Reviewed:****Description:**We provide new characterizations of the

About error bounds in metrizable topological vector spaces

- Abbasi, Malek, Théra, Michel

**Authors:**Abbasi, Malek , Théra, Michel**Date:**2022**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 30, no. 4 (2022), p. 1291-1311**Full Text:****Reviewed:****Description:**This paper aims to present some sufficient criteria under which a given function between two spaces that are either topological vector spaces whose topologies are generated by metrics or metrizable subsets of some topological vector spaces, satisfies the error bound property. Then, we discuss the Hoffman estimation and obtain some results for the estimate of the distance to the set of solutions to a system of linear equalities. The advantage of our estimate is that it allows to calculate the coefficient of the error bound. The applications of this presentation are illustrated by some examples. © 2022, This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply.

**Authors:**Abbasi, Malek , Théra, Michel**Date:**2022**Type:**Text , Journal article**Relation:**Set-Valued and Variational Analysis Vol. 30, no. 4 (2022), p. 1291-1311**Full Text:****Reviewed:****Description:**This paper aims to present some sufficient criteria under which a given function between two spaces that are either topological vector spaces whose topologies are generated by metrics or metrizable subsets of some topological vector spaces, satisfies the error bound property. Then, we discuss the Hoffman estimation and obtain some results for the estimate of the distance to the set of solutions to a system of linear equalities. The advantage of our estimate is that it allows to calculate the coefficient of the error bound. The applications of this presentation are illustrated by some examples. © 2022, This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply.

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