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**Date:** 2017
**Subject:** 0102 Applied Mathematics | 0801 Artificial Intelligence and Image Processing | 0906 Electrical and Electronic Engineering | E-commerce | Fuzzy reasoning | Multiple linear regression | Negotiation decision functions (NDFs) | Online auctions | Software agents
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/159259
**Description:** Bidders often feel challenged when looking for the best bidding strategies to excel in the competitive environment of multiple and simultaneous online auctions for same or similar items. Bidders face ... More
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**Date:** 2017
**Subject:** 0101 Pure Mathematics | 0102 Applied Mathematics | Topological group | Locally compact group | pro-Lie group | Separable topological space
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/159323
**Description:** We give a complete characterization of subgroups of separable topological groups. Then we show that the following conditions are equivalent for an omega-narrow topological group G: (i) G is homeomorph... More
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**Date:** 2017
**Subject:** 0102 Applied Mathematics | 0905 Civil Engineering | 0912 Materials Engineering | Nonlinear elasticity | Convexity | Global minimizers | Second Piola-Kirchhoff stress tensor
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/159312
**Description:** We present a sufficient condition under which a weak solution of the Euler-Lagrange equations in nonlinear elasticity is already a global minimizer of the corresponding elastic energy functional. This... More
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**Authors:**
Gao, David
**Date:** 2016
**Subject:** 0102 Applied Mathematics | 0915 Interdisciplinary Engineering | Canonical duality-triality | Complementary variational principle | Nonconvex analysis | Nonlinear elasticity | Nonlinear PDEs
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/99896
**Description:** This paper presents a pure complementary energy variational method for solving a general anti-plane shear problem in finite elasticity. Based on the canonical dualityâ€“triality theory developed by th... More
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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:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Canonical duality theory | CEC benchmark | Constrained optimization | Global optimization
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/100713
**Description:** This paper aims to solve a class of CEC benchmark constrained optimization problems that have been widely studied by nature-inspired optimization algorithms. Based on canonical duality theory, these c... More
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**Date:** 2016
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | 0802 Computation Theory and Mathematics | Canonical duality theory | Double-well function | Global optimization | Log-sum-exp function | Minimax problems | Polynomial minimisation
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/100457
**Description:** This paper presents a canonical dual approach for solving a nonconvex global optimization problem governed by a sum of 4th-order polynomial and a log-sum-exp function. Such a problem arises extensivel... More
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**Date:** 2016
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Aubin property | Calmness | Directional limiting coderivative | Solution map | Software engineering | Aubin properties | Fine analysis | Implicit function | Implicit multifunctions | Lipschitzian | Nocv1 | Polyhedral set | Computer science
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154327
**Description:** This paper is devoted to the development of new sufficient conditions for the calmness and the Aubin property of implicit multifunctions. As the basic tool we employ the directional limiting coderivat... More
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**Date:** 2016
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Sum and pointwise supremum of convex functions | Fenchel and approximate subdifferentials
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154567
**Description:** We give a formula for the subdifferential of the sum of two convex functions where one of them is the supremum of an arbitrary family of convex functions. This is carried out under a weak assumption e... More
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**Date:** 2015
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Metric regularity | Induction theorem | Ekeland variational principle | Optimality conditions
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/100394
**Description:** A general nonlinear regularity model for a set-valued mapping F : X x R+ paired right arrows Y, where X and Y are metric spaces, is studied using special iteration procedures, going back to Banach, Sc... More
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**Date:** 2015
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | 0802 Computation Theory and Mathematics | Error bound property | Generalized equations | Perturbation stability | Relative/directional metric regularity | Semicontinuous envelope | Directional metric regularity | Distance functions | Error bound | Generalized Equations | Lower semicontinuous | Metric regularity | Semi-continuous | Set-valued mapping | Mapping
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/98984
**Description:** In this paper, we study relative metric regularity of set-valued mappings with emphasis on directional metric regularity. We establish characterizations of relative metric regularity without assuming ... More
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**Authors:**
Kruger, Alexander
**Date:** 2015
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Calmness | Error bounds | Metric regularity | Metric subregularity | Slope
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/76402
**Description:** Necessary and sufficient criteria for metric subregularity (or calmness) of set-valued mappings between general metric or Banach spaces are treated in the framework of the theory of error bounds for a... More
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**Date:** 2015
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | Constrained polynomial programming | Problem | Necessary global optimality condition | Linear
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/92549
**Description:** The general constrained polynomial programming problem (GPP) is considered in this paper. Problem (GPP) has a broad range of applications and is proved to be NP-hard. Necessary global optimality condi... More
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**Date:** 2015
**Subject:** 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics | 0906 Electrical and Electronic Engineering | Collections of sets | Metric regularity | Normal cone | Subdifferential
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/92572
**Description:** Several primal and dual quantitative characterizations of regularity properties of collections of sets in normed linear spaces are discussed. Relationships between regularity properties of collections... More
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**Date:** 2015
**Subject:** Conic programming | Generalized differentiation | Isolated calmness | Optimality conditions | Second-order theory | Tilt stability | Variational analysis | 0102 Applied Mathematics | 0103 Numerical and Computational Mathematics
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/77111
**Description:** This paper is devoted to the study of a broad class of problems in conic programming modeled via parameter-dependent generalized equations. In this framework we develop a second-order generalized diff... More
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Second-order variational analysis in conic programming with applications to optimality and stability