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**Date:** 2017
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/155253
**Description:** In this paper the relation between the weak subdifferentials and the directional derivatives, as well as optimality conditions for nonconvex optimization problems in reflexive Banach spaces, are inves... More
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**Date:** 2016
**Subject:** 0101 Pure Mathematics | Pro-Lie group | Locally compact abelian group | Open mapping theorem
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154692
**Description:** It is proved that any surjective morphism f : Z(k) -> K onto a locally compact group K is open for every cardinal k. This answers a question posed by Hofmann and the second author.
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**Date:** 2016
**Subject:** 0101 Pure Mathematics | 0102 Applied Mathematics | 0906 Electrical and Electronic Engineering | Borwein-Preiss variational principle | Smooth variational principle | Gauge-type function | Perturbation
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/100317
**Description:** In this article, we refine and slightly strengthen the metric space version of the Borwein-Preiss variational principle due to Li and Shi (2000) [12], clarify the assumptions and conclusions of their ... More
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**Date:** 2016
**Subject:** 0101 Pure Mathematics | 0802 Computation Theory and Mathematics | Compact groups | Subgroups
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/99916
**Description:** In 1985 S. Saeki and K. Stromberg published the following question: Does every infinite compact group have a subgroup which is not Haar measurable? An affirmative answer is given for all compact group... More
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**Date:** 2015
**Subject:** 0101 Pure Mathematics | Maximally monotone operator | ε-subdifferential mapping | Subdifferential operator | Convex lower semicontinuous function | Fitzpatrick function | Enlargement of an operator | Brøndsted- Rockafellar enlargements | Additive enlargements | Fenchel-Young function
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/100313
**Description:** We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the ... More
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**Authors:**
Kruger, Alexander
**Date:** 2015
**Subject:** 0101 Pure Mathematics | Error bounds | Hölder metric subregularity | Metric regularity | Metric subregularity | Slope
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/155338
**Description:** The Holder setting of the metric subregularity property of set-valued mappings between general metric or Banach/Asplund spaces is investigated in the framework of the theory of error bounds for extend... More
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**Date:** 2015
**Subject:** 0101 Pure Mathematics | Variational analysis and optimization | Parameterized equilibria | Conic constraints | Sensitivity and stability analysis | Solution maps | Graphical derivatives | Normal and tangent cones
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/100365
**Description:** The paper concerns parameterized equilibria governed by generalized equations whose multivalued parts are modeled via regular normals to nonconvex conic constraints. Our main goal is to derive a preci... More
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**Date:** 2014
**Subject:** 0101 Pure Mathematics | 0102 Applied Mathematics | 0906 Electrical and Electronic Engineering | Metric regularity | Uniform regularity | Normal cone | Subdifferential
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/92587
**Description:** We examine three primal space local Holder type regularity properties of finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and uniform [q]-regularity as well as their quantita... More
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**Date:** 2014
**Subject:** Constant rank constraint qualification | Constraint qualifications | Lagrange multipliers | Mangasarian-Fromovitz constraint qualification | Nonlinear programming | Regularity conditions | 0101 Pure Mathematics | 0102 Applied Mathematics
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/155269
**Description:** For the classical nonlinear program, two new relaxations of the Mangasarian– Fromovitz constraint qualification are discussed and their relationship with some standard constraint qualifications is exa... More
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**Date:** 2013
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/61886
**Description:** The present article continues the investigation of constructions essential for applications of combinatorial semigroups to the design of multiple classification systems in data mining. Our main theore... More
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**Date:** 2013
**Subject:** 0101 Pure Mathematics | 0102 Applied Mathematics | Billiards | Invisibility in geometrical optics | Problems of minimal resistance
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/38905
**Description:** We study the problem of invisibility for bodies with a mirror surface in the framework of geometrical optics. We show that for any two given directions it is possible to construct a two-dimensional fr... More
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**Date:** 2013
**Subject:** 0101 Pure Mathematics | 0102 Applied Mathematics | Bipartite Moore bound | Defect | Degree/diameter problem for bipartite graphs | Large bipartite graphs
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/44102
**Description:** We consider the bipartite version of the degree/diameter problem, namely, given natural numbers dâ‰¥2 and Dâ‰¥2, find the maximum number N b(d,D) of vertices in a bipartite graph of maximum degree d a... More
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**Date:** 2012
**Subject:** Variational analysis | Error Bounds | Slope | Vector variational principle | 0101 Pure Mathematics
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/155230
**Description:** In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new ... More
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**Date:** 2012
**Subject:** 0101 Pure Mathematics | Aubin property | Calmness | Generalized equations | Hoelder stability | Iteration schemes | Variational principles
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/55174
**Description:** We show in a rather general setting that Hoelder and Lipschitz stability properties of solutions to variational problems can be characterized by convergence of more or less abstract iteration schemes.... More
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**Date:** 2012
**Subject:** Classification and clustering | Rees matrix semigroups | Sets of centroids | 0101 Pure Mathematics
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/63531
**Description:** Abstract We introduce a new construction involving Rees matrix semigroups and max-plus algebras that is very convenient for generating sets of centroids. We describe completely all optimal sets of cen... More
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