On Fréchet subdifferentials
- Authors: Kruger, Alexander
- Date: 2003
- Type: Text , Journal article
- Relation: Journal of Mathematical Sciences Vol. 116, no. 3 (2003), p. 3325-3358
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- Description: 2003002852
Weak stationarity : Eliminating the gap between necessary and sufficient conditions
- Authors: Kruger, Alexander
- Date: 2004
- Type: Text , Journal article
- Relation: Optimization Vol. 53, no. 2 (Apr 2004), p. 147-164
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- Description: Starting from known necessary extremality conditions in terms of strict subdifferentials and normals the notion of weak stationarity is introduced. It is defined in terms of initial space elements. The necessary conditions become necessary and sufficient (for stationarity).
- Description: 2003000887
A new algorithm for the placement of WLAN access point based on nonsmooth optimization technique
- Authors: Kouhbor, Shahnaz , Ugon, Julien , Kruger, Alexander , Rubinov, Alex , Branch, Philip
- Date: 2005
- Type: Text , Conference paper
- Relation: Paper presented at the 7th International Conference on Advanced Communication Technology, Phoenix Park, Korea : 21st February, 2005
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- Description: In wireless local area network (WLAN), signal coverage is obtained by proper placement of access points (APs). The impact of incorrect placement of APs is significant. If they are placed too far apart, they generate a coverage gap but if they are too close to each other, this leads to excessive co-channel interferences. In this paper, we describe a mathematical model we have developed to find the optimal number and location of APs. To solve the problem, we use an optimization algorithm developed at the University of Ballarat called discrete gradient algorithm. Results indicate that our model is able to solve optimal coverage problems for different numbers of users.
- Description: E1
- Description: 2003001376
Optimal placement of access point in WLAN based on a new algorithm
- Authors: Kouhbor, Shahnaz , Ugon, Julien , Kruger, Alexander , Rubinov, Alex
- Date: 2005
- Type: Text , Conference paper
- Relation: Paper presented at ICMB 2005, International Conference on Mobile Business, Sydney, Australia, 11-13 July 2005, Sydney : 11th - 13th July, 2005
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- Description: When designing wireless communication systems, it is very important to know the optimum numbers and locations for the access points (APs). The impact of incorrect placement of APs is significant. If they are placed too far apart, they will generate a coverage gap, but if they are too close to each other, this will lead to excessive co-channel interferences. In this paper we describe a mathematical model developed to find the optimal number and location of APs. To solve the problem, we use the Discrete Gradient optimization algorithm developed at the University of Ballarat. Results indicate that our model is able to solve optimal coverage problems for different numbers of users.
- Description: 2003001377
Stationarity and regularity of set systems
- Authors: Kruger, Alexander
- Date: 2005
- Type: Text , Journal article
- Relation: Pacific Journal of Optimization Vol. 1, no. 1 (2005), p. 101-126
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- Description: Extremality, stationarity and regularity notions for a system of closed sets in a normed linear space are investigated. The equivalence of different abstract “extremal” settings in terms of set systems and multifunctions is proved. The dual necessary and sufficient conditions of weak stationarity (the Extended extremal principle) are presented for the case of an Asplund space.
- Description: 2003001378
About regularity of collections of sets
- Authors: Kruger, Alexander
- Date: 2006
- Type: Text , Journal article
- Relation: Set-Valued Analysis Vol. 14, no. 2 (Jun 2006), p. 187-206
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- Description: The paper continues investigations of stationarity and regularity properties of collections of sets in normed spaces. It contains a summary of different characterizations (both primal and dual) of regularity and a list of sufficient conditions for a collection of sets to be regular.
- Description: 2003001526
Coverage in WLAN : Optimization model and algorithm
- Authors: Kouhbor, Shahnaz , Ugon, Julien , Mammadov, Musa , Rubinov, Alex , Kruger, Alexander
- Date: 2006
- Type: Text , Conference paper
- Relation: Paper presented at the First International Conference on Wireless Broadband and Ultra Wideband Communications, AusWireless 2006, Sydney : 13th March, 2006
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- Description: When designing wireless communication systems, it is very important to know the optimum numbers of access points (APs) in order to provide a reliable design. In this paper we describe a mathematical model developed for finding the optimal number and location of APs. A new Global Optimization Algorithm (AGOP) is used to solve the problem. Results obtained demonstrate that the model and software are able to solve optimal coverage problems for design areas with different types of obstacles and number of users.
- Description: 2003001757
Coverage in WLAN with minimum number of access points
- Authors: Kouhbor, Shahnaz , Ugon, Julien , Rubinov, Alex , Kruger, Alexander , Mammadov, Musa
- Date: 2006
- Type: Text , Conference paper
- Relation: Paper presented at VTC 2006 - Spring, 2006 IEEE 63rd Vehicular Technology Conference, Melbourne : 7th May, 2006
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- Description: E1
- Description: 2003001610
Stationarity and regularity concepts for set systems
- Authors: Kruger, Alexander , University of Ballarat
- Date: 2006
- Type: Journal article
- Relation: IFIP International Federation for Information Processing
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- Description: Extremality, stationarity and regularity notions for a system of closed sets in a normed linear space are investigated. The equivalence of different abstract “extremal” settings in terms of set systems and multifunctions is proved. The dual necessary and sufficient conditions of weak stationarity (the Extended extremal principle) are presented for the case of an Asplund space.
Facility location via continuous optimization with discontinuous objective functions
- Authors: Ugon, Julien , Kouhbor, Shahnaz , Mammadov, Musa , Rubinov, Alex , Kruger, Alexander
- Date: 2007
- Type: Text , Journal article
- Relation: ANZIAM Journal Vol. 48, no. 3 (2007), p. 315-325
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- Description: Facility location problems are one of the most common applications of optimization methods. Continuous formulations are usually more accurate, but often result in complex problems that cannot be solved using traditional optimization methods. This paper examines the use of a global optimization method - AGOP - for solving location problems where the objective function is discontinuous. This approach is motivated by a real-world application in wireless networks design. © Australian Mathematical Society 2007.
- Description: 2003004859
Boris Mordukhovich, the never tiring traveller, celebrates his sixtieth birthday
- Authors: Henrion, René , Kruger, Alexander , Outrata, Jiri
- Date: 2008
- Type: Text , Journal article
- Relation: Set-Valued Analysis Vol. 16, no. 2-3 (2008), p. 125-127
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Metric regularity and systems of generalized equations
- Authors: Dmitruk, Andrei , Kruger, Alexander
- Date: 2008
- Type: Text , Journal article
- Relation: Journal of Mathematical Analysis and Applications Vol. 342, no. 2 (2008), p. 864-873
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- Description: The paper is devoted to a revision of the metric regularity property for mappings between metric or Banach spaces. Some new concepts are introduced: uniform metric regularity and metric multi-regularity for mappings into product spaces, when each component is perturbed independently. Regularity criteria are established based on a nonlocal version of Lyusternik-Graves theorem due to Milyutin. The criteria are applied to systems of generalized equations producing some "error bound" type estimates. © 2007 Elsevier Inc. All rights reserved.
Error bounds : Necessary and sufficient conditions
- Authors: Fabian, Marian , Henrion, René , Kruger, Alexander , Outrata, Jiri
- Date: 2010
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 18, no. 2 (2010), p. 121-149
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- Description: The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space. © 2010 Springer Science+Business Media B.V.
Stability of error bounds for convex constraints systems in Banach spaces
- Authors: Thera, Michel , Van Ngai, Huynh , Kruger, Alexander
- Date: 2010
- Type: Text , Journal article
- Relation: SIAM Journal on Optimization Vol. 20, no. 6 (2010), p. 3280-3296
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- Description: This paper studies stability of error bounds for convex constraints in Banach spaces. We show that certain known sufficient conditions for local and global error bounds actually ensure error bounds for the family of functions being in a sense small perturbations of the given one. A single inequality as well as semi-infinite constraint systems are considered.
- Description: C1
Stability of error bounds for semi-infinite convex constraint systems
- Authors: Van Ngai, Huynh , Kruger, Alexander , Théra, Michel
- Date: 2010
- Type: Text , Journal article
- Relation: SIAM Journal on Optimization Vol. 20, no. 4 (2010), p. 2080-2096
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- Description: In this paper, we are concerned with the stability of the error bounds for semi-infinite convex constraint systems. Roughly speaking, the error bound of a system of inequalities is said to be stable if all its "small" perturbations admit a (local or global) error bound. We first establish subdifferential characterizations of the stability of error bounds for semi-infinite systems of convex inequalities. By applying these characterizations, we extend some results established by Azé and Corvellec [SIAM J. Optim., 12 (2002), pp. 913-927] on the sensitivity analysis of Hoffman constants to semi-infinite linear constraint systems. Copyright © 2010, Society for Industrial and Applied Mathematics.
About errors bounds in metric spaces
- Authors: Fabian, Marian , Henrion, René , Kruger, Alexander , Outrata, Jiri
- Date: 2011
- Type: Text , Conference paper
- Relation: International Conference Operations Research p. 33-38
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: The paper presents a general primal space classification scheme of necessary and suffficient criteria for the error bound property incorporating the existing conditions. Several primal space derivative-like objects - slopes are used to characterize the error bound property of extended-real valued functions on metric sapces.
Calmness of efficient solution maps in parametric vector optimization
- Authors: Chuong, Thai Doan , Kruger, Alexander , Yao, J. C.
- Date: 2011
- Type: Journal article
- Relation: Journal of Global Optimization Vol. 51, no. 4 (2011), p. 677-688
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: The paper is concerned with the stability theory of the efficient solution map of a parametric vector optimization problem. Utilizing the advanced tools of modern variational analysis and generalized differentiation, we study the calmness of the efficient solution map. More explicitly, new sufficient conditions in terms of the Fréchet and limiting coderivatives of parametric multifunctions for this efficient solution map to have the calmness at a given point in its graph are established by employing the approach of implicit multifunctions. Examples are also provided for analyzing and illustrating the results obtained. © 2011 Springer Science+Business Media, LLC.
Comments on : Stability in linear optimization and related topics. A personal tour
- Authors: Kruger, Alexander
- Date: 2012
- Type: Text , Journal article
- Relation: TOP Vol. 20, no. 2 (2012), p. 255-257
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- Description: The article presents a report on a wonderful tour in the area of stability analysis of linear (and not only linear) optimization undertaken in the last 15 years by the author and his team of collaborators. 15 years is a very short period for developing a mathematical theory. Nevertheless the scope of achievement presented in the article and the level of development of the theory are really impressive. The tour is full of attractions and the route is very carefully marked. Now the tour is on offer, and the author is eager to share its highlights with interested travelers.
Error bounds for vector-valued functions : Necessary and sufficient conditions
- Authors: Bednarczuk, Ewa , Kruger, Alexander
- Date: 2012
- Type: Text , Journal article
- Relation: Nonlinear Analysis, Theory, Methods and Applications Vol. 75, no. 3 (2012), p. 1124-1140
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- 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 derivative-like objects (slopes and subdifferentials) are introduced and a general classification scheme of error bound criteria is presented.
- 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 derivative-like objects (slopes and subdifferentials) are introduced and a general classification scheme of error bound criteria is presented. © 2011 Elsevier Ltd. All rights reserved.
Error bounds for vector-valued funtions on metric spaces
- Authors: Kruger, Alexander , Bednarczuk, Ewa
- Date: 2012
- Type: Text , Journal article
- Relation: Vietnam Journal of Mathematics Vol. 40, no. 2/3 (2012), p. 165-180
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- 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 primal space derivative-like objects – slopes – are introduced and a classification scheme of error bound criteria is presented.