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
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.
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
About stationarity and regularity of real-valued functions
- Authors: Kruger, Alexander
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at ICOTA6: 6th International Conference on Optimization - Techniques and Applications, Ballarat, Victoria : 9th December, 2004
- Full Text: false
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- Description: 2003000888
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
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.
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.
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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Extensions of metric regularity
- Authors: Dmitruk, Andrei , Kruger, Alexander
- Date: 2009
- Type: Text , Journal article
- Relation: Optimization Vol. 58, no. 5 (2009), p. 561-584
- Full Text: false
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- Description: This article is devoted to some extensions of the metric regularity property for mappings between metric or Banach spaces. Several new concepts are investigated in a unified manner: uniform metric regularity, metric regularity along a subspace, metric multi-regularity for mappings into product spaces (when each component is perturbed independently), as well as their Lipschitz-like counterparts. The properties are characterized in terms of certain derivative-like constants. Regularity criteria are established based on a set-valued extension of a nonlocal version of the Lyusternik-Graves theorem due to Milyutin.
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.
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
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
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
Nonsmooth analysis : Fréchet subdifferentials
- Authors: Kruger, Alexander
- Date: 2009
- Type: Text , Book chapter
- Relation: Encyclopedia of Optimization Chapter p. 2651-2658
- Full Text: false
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
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
- Full Text:
- Reviewed:
- 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
Optimization in wireless local area network
- Authors: Kouhbor, Shahnaz , Ugon, Julien , Kruger, Alexander , Rubinov, Alex , Branch, Philip
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at ICOTA6: 6th International Conference on Optimization - Techniques and Applications, Ballarat, Victoria : 9th December, 2004
- Full Text: false
- Reviewed:
- Description: 2003000886
Nonsmooth analysis : Weak stationarity
- Authors: Kruger, Alexander
- Date: 2009
- Type: Text , Book chapter
- Relation: Encyclopedia of Optimization Chapter p. 2658-2664
- Full Text: false
- Description: The article considers stationary and regularity concepts for extended real-valued functions on metric spaces.
Special Issue on recent advances in continuous optimization on the occasion of the 25th European conference on Operational Research (EURO XXV 2012)
- Authors: Weber, Gerhard-Wilhelm , Kruger, Alexander , Martinez-Legaz, Juan , Mordukhovich, Boris , Sakalauskas, Leonidas
- Date: 2014
- Type: Text , Journal article
- Relation: Optimization Vol. 63, no. 1 (2014), p. 1-5
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Error bounds and metric subregularity
- Authors: Kruger, Alexander
- Date: 2015
- Type: Text , Journal article
- Relation: Optimization Vol. 64, no. 1 (2015), p. 49-79
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- 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 special family of extended real-valued functions of two variables. A classification scheme for the general error bound and metric subregularity criteria is presented. The criteria are formulated in terms of several kinds of primal and subdifferential slopes.