Conical averagedness and convergence analysis of fixed point algorithms
- Authors: Bartz, Sedi , Dao, Minh , Phan, Hung
- Date: 2022
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol. 82, no. 2 (2022), p. 351-373
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- Description: We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the stability under relaxations, convex combinations and compositions. We derive conical averagedness properties of resolvents of generalized monotone operators. These properties are then utilized in order to analyze the convergence of the proximal point algorithm, the forward–backward algorithm, and the adaptive Douglas–Rachford algorithm. Our study unifies, improves and casts new light on recent studies of these topics. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
Changes in the chemistry of sedimentary organic matter within the Coorong over space and time
- Authors: Krull, Evelyn , Haynes, Deborah , Lamontagne, Sebastien , Gell, Peter , McKirdy, David , Hancock, Gary , McGowan, Janine , Smernik, Ronald
- Date: 2009
- Type: Text , Journal article
- Relation: Biogeochemistry Vol. 92, no. 1-2 (2009), p. 9-25
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- Description: Like many other coastal systems across the world, the Coorong lagoonal ecosystem (South Australia) has degraded over the last 100 years; in this case as a result of extensive regulation and diversions of water across the Murray-Darling Basin following European settlement. To evaluate whether the sources of organic matter (OM) supporting its food-web have changed since the inception of water management and barrage construction, sedimentary OM was characterised in cores spanning the Coorong’s salinity gradient at depths representative of the last 100 years over which the management alterations to river and estuarine flow were most marked. Detailed 210Pb, 137Cs and Pu dating in conjunction with palaeolimnological data (Pinus pollen) allowed for the reconstruction of the timing of substantial changes observed in the composition of the OM, most of which occur during the early 1950s, concurrent with management-related variations in water flow and salinity. Negative shifts in
On large bipartite graphs of diameter 3
- Authors: Feria-Purón, Ramiro , Miller, Mirka , Pineda-Villavicencio, Guillermo
- Date: 2013
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 313, no. 4 (2013), p. 381-390
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: We consider the bipartite version of the degree/diameter problem, namely, given natural numbers d≥2 and D≥2, find the maximum number N b(d,D) of vertices in a bipartite graph of maximum degree d and diameter D. In this context, the bipartite Moore bound Mb(d,D) represents a general upper bound for Nb(d,D). Bipartite graphs of order Mb(d,D) are very rare, and determining Nb(d,D) still remains an open problem for most (d,D) pairs. This paper is a follow-up of our earlier paper (Feria-Purón and Pineda-Villavicencio, 2012 [5]), where a study on bipartite (d,D,-4)-graphs (that is, bipartite graphs of order M b(d,D)-4) was carried out. Here we first present some structural properties of bipartite (d,3,-4)-graphs, and later prove that there are no bipartite (7,3,-4)-graphs. This result implies that the known bipartite (7,3,-6)-graph is optimal, and therefore Nb(7,3)=80. We dub this graph the Hafner-Loz graph after its first discoverers Paul Hafner and Eyal Loz. The approach here presented also provides a proof of the uniqueness of the known bipartite (5,3,-4)-graph, and the non-existence of bipartite (6,3,-4)-graphs. In addition, we discover at least one new largest known bipartite-and also vertex-transitive-graph of degree 11, diameter 3 and order 190, a result which improves by four vertices the previous lower bound for Nb(11,3). © 2012 Elsevier B.V. All rights reserved.
- Description: 2003011037
Magic and antimagic labeling of graphs
- Authors: Sugeng, Kiki Ariyanti
- Date: 2005
- Type: Text , Thesis , PhD
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- Description: "A bijection mapping that assigns natural numbers to vertices and/or edges of a graph is called a labeling. In this thesis, we consider graph labelings that have weights associated with each edge and/or vertex. If all the vertex weights (respectively, edge weights) have the same value then the labeling is called magic. If the weight is different for every vertex (respectively, every edge) then we called the labeling antimagic. In this thesis we introduce some variations of magic and antimagic labelings and discuss their properties and provide corresponding labeling schemes. There are two main parts in this thesis. One main part is on vertex labeling and the other main part is on edge labeling."
- Description: Doctor of Philosophy
On graphs of defect at most 2
- Authors: Feria-Purón, Ramiro , Miller, Mirka , Pineda-Villavicencio, Guillermo
- Date: 2011
- Type: Text , Journal article
- Relation: Discrete Applied Mathematics Vol. 159, no. 13 (2011), p. 1331-1344
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- Description: In this paper we consider the degree/diameter problem, namely, given natural numbers Δ<2 and D<1, find the maximum number N(Δ,D) of vertices in a graph of maximum degree Δ and diameter D. In this context, the Moore bound M(Δ,D) represents an upper bound for N(Δ,D). Graphs of maximum degree Δ, diameter D and order M(Δ,D), called Moore graphs, have turned out to be very rare. Therefore, it is very interesting to investigate graphs of maximum degree Δ<2, diameter D<1 and order M(Δ,D)- with small >0, that is, (Δ,D,-)-graphs. The parameter is called the defect. Graphs of defect 1 exist only for Δ=2. When >1, (Δ,D,-)-graphs represent a wide unexplored area. This paper focuses on graphs of defect 2. Building on the approaches developed in Feria-Purón and Pineda-Villavicencio (2010) [11] we obtain several new important results on this family of graphs. First, we prove that the girth of a (Δ,D,-2)-graph with Δ<4 and D<4 is 2D. Second, and most important, we prove the non-existence of (Δ,D,-2)-graphs with even Δ<4 and D<4; this outcome, together with a proof on the non-existence of (4,3,-2)-graphs (also provided in the paper), allows us to complete the catalogue of (4,D,-)-graphs with D<2 and 0≤≤2. Such a catalogue is only the second census of (Δ,D,-2)-graphs known at present, the first being that of (3,D,-)-graphs with D<2 and 0≤≤2 Jørgensen (1992) [14]. Other results of this paper include necessary conditions for the existence of (Δ,D,-2)-graphs with odd Δ<5 and D<4, and the non-existence of (Δ,D,-2)-graphs with odd Δ<5 and D<5 such that Δ≡0,2(modD). Finally, we conjecture that there are no (Δ,D,-2)-graphs with Δ<4 and D<4, and comment on some implications of our results for the upper bounds of N(Δ,D). © 2011 Elsevier B.V. All rights reserved.
On bipartite graphs of defect 2
- Authors: Delorme, Charles , Jorgensen, Leif , Miller, Mirka , Pineda-Villavicencio, Guillermo
- Date: 2009
- Type: Text , Journal article
- Relation: European Journal of Combinatorics Vol. 30, no. 4 (2009), p. 798-808
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- Description: It is known that the Moore bipartite bound provides an upper bound on the order of a connected bipartite graph. In this paper we deal with bipartite graphs of maximum degree
An adaptive splitting algorithm for the sum of two generalized monotone operators and one cocoercive operator
- Authors: Dao, Minh , Phan, Hung
- Date: 2021
- Type: Text , Journal article
- Relation: Fixed Point Theory and Algorithms for Sciences and Engineering Vol. 2021, no. 1 (2021), p.
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- Description: Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward steps involve the operators implicitly via their resolvents. In this paper, we study an adaptive splitting algorithm for finding a zero of the sum of three operators. We assume that two of the operators are generalized monotone and their resolvents are computable, while the other operator is cocoercive but its resolvent is missing or costly to compute. Our splitting algorithm adapts new parameters to the generalized monotonicity of the operators and, at the same time, combines appropriate forward and backward steps to guarantee convergence to a solution of the problem. © 2021, The Author(s).
Complete catalogue of graphs of maximum degree 3 and defect at most 4
- Authors: Miller, Mirka , Pineda-Villavicencio, Guillermo
- Date: 2009
- Type: Text , Journal article
- Relation: Discrete Applied Mathematics Vol. 157, no. 13 (2009), p. 2983-2996
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- Description: We consider graphs of maximum degree 3, diameter D≥2 and at most 4 vertices less than the Moore bound M3,D, that is, (3,D,−)-graphs for ≤4. We prove the non-existence of (3,D,−4)-graphs for D≥5, completing in this way the catalogue of (3,D,−)-graphs with D≥2 and ≤4. Our results also give an improvement to the upper bound on the largest possible number N3,D of vertices in a graph of maximum degree 3 and diameter D, so that N3,D≤M3,D−6 for D≥5. Copyright Elsevier.
On bipartite graphs of defect at most 4
- Authors: Feria-Purón, Ramiro , Pineda-Villavicencio, Guillermo
- Date: 2011
- Type: Text , Journal article
- Relation: Discrete Applied Mathematics Vol.160, no.1-2 (2011), p.140-154
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- Description: We consider the bipartite version of the degree/diameter problem, namely, given natural numbers Δ ≥ 2 and D ≥ 2, find the maximum number Nb (Δ, D) of vertices in a bipartite graph of maximum degree Δ and diameter D. In this context, the Moore bipartite bound Mb (Δ, D) represents an upper bound for Nb (Δ, D). Bipartite graphs of maximum degree Δ, diameter D and order Mb (Δ, D)-called Moore bipartite graphs-have turned out to be very rare. Therefore, it is very interesting to investigate bipartite graphs of maximum degree Δ ≥ 2, diameter D ≥ 2 and order Mb (Δ, D) - ε{lunate} with small ε{lunate} > 0, that is, bipartite (Δ, D, - ε{lunate})-graphs. The parameter ε{lunate} is called the defect. This paper considers bipartite graphs of defect at most 4, and presents all the known such graphs. Bipartite graphs of defect 2 have been studied in the past; if Δ ≥ 3 and D ≥ 3, they may only exist for D = 3. However, when ε{lunate} > 2 bipartite (Δ, D, - ε{lunate})-graphs represent a wide unexplored area. The main results of the paper include several necessary conditions for the existence of bipartite (Δ, D, - 4)-graphs; the complete catalogue of bipartite (3, D, - ε{lunate})-graphs with D ≥ 2 and 0 ≤ ε{lunate} ≤ 4; the complete catalogue of bipartite (Δ, D, - ε{lunate})-graphs with Δ ≥ 2, 5 ≤ D ≤ 187 (D ≠6) and 0 ≤ ε{lunate} ≤ 4; a proof of the non-existence of all bipartite (Δ, D, - 4)-graphs with Δ ≥ 3 and odd D ≥ 5. Finally, we conjecture that there are no bipartite graphs of defect 4 for Δ ≥ 3 and D ≥ 5, and comment on some implications of our results for the upper bounds of Nb (Δ, D). © 2011 Elsevier B.V. All rights reserved.
The molecular epidemiology of influenza in Cambodia
- Authors: Suttie, Annika
- Date: 2019
- Type: Text , Thesis , PhD
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- Description: Avian influenza viruses (AIVs) represent a risk to the health of humans and animals. The prevalence of AIVs in live bird markets in Cambodia is among the highest in the world, being detected in 45.5% of tested poultry in 2015. To better understand the potential risk presented by AIVs, this thesis investigated the genetic characteristics of AIVs circulating in Cambodia between 2014 to 2018; focusing on subtypes that pose the greatest risk to human and animal health (H5, H7 and H9). Highly pathogenic (HP) H5N1 clade 2.3.2.1c viruses and low pathogenic H9N2 BJ/94-like h9-4.2.5 clade viruses were the most frequently detected subtypes, and circulate endemically in Cambodia’s domestic poultry. Co-infections were detected and facilitated the production of two novel reassortant H5N1 AIVs with single genes from H9N2 viruses. Additionally, numerous intrasubtypic reassortment events were detected for H5 and H9 AIVs. This is concerning as reassortment events can rapidly produce novel viruses of public health risk. Phylogenetic analyses showed some genes of the Cambodian H5, H7 and H9 AIVs clustered with zoonotic viruses, suggesting a common origin. There are parallels between H5N1 and H9N2 AIVs detected in Cambodia and Vietnam, likely facilitated through the illegal trade of live poultry and/or the migration of wild birds. Molecular analyses showed H9 AIVs have major markers associated with adaptation to mammals; though during the study period the only human AIV cases were the result of HP H5N1. Molecular markers of resistance to adamantine antivirals was observed in 3% of H5 and 41% of H9 AIVs; however, both subtypes remain susceptible to first line antiviral treatment, neuraminidase inhibitors. The data presented in this thesis demonstrates that circulation of Cambodian AIVs represents a risk for the emergence of novel viruses. Interventions are urgently needed to mitigate the threat posed to poultry and humans.
- Description: Doctor of Philosophy
Structural properties and labeling of graphs
- Authors: Dafik
- Date: 2007
- Type: Text , Thesis , PhD
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- Description: The complexity in building massive scale parallel processing systems has re- sulted in a growing interest in the study of interconnection networks design. Network design affects the performance, cost, scalability, and availability of parallel computers. Therefore, discovering a good structure of the network is one of the basic issues. From modeling point of view, the structure of networks can be naturally stud- ied in terms of graph theory. Several common desirable features of networks, such as large number of processing elements, good throughput, short data com- munication delay, modularity, good fault tolerance and diameter vulnerability correspond to properties of the underlying graphs of networks, including large number of vertices, small diameter, high connectivity and overall balance (or regularity) of the graph or digraph. The first part of this thesis deals with the issue of interconnection networks ad- dressing system. From graph theory point of view, this issue is mainly related to a graph labeling. We investigate a special family of graph labeling, namely antimagic labeling of a class of disconnected graphs. We present new results in super (a; d)-edge antimagic total labeling for disjoint union of multiple copies of special families of graphs. The second part of this thesis deals with the issue of regularity of digraphs with the number of vertices close to the upper bound, called the Moore bound, which is unobtainable for most values of out-degree and diameter. Regularity of the underlying graph of a network is often considered to be essential since the flow of messages and exchange of data between processing elements will be on average faster if there is a similar number of interconnections coming in and going out of each processing element. This means that the in-degree and out-degree of each processing element must be the same or almost the same. Our new results show that digraphs of order two less than Moore bound are either diregular or almost diregular.
- Description: Doctor of Philosophy
On relaxing the Mangasarian-Fromovitz constraint qualification
- Authors: Kruger, Alexander , Minchenko, Leonld , Outrata, Jiri
- Date: 2014
- Type: Text , Journal article
- Relation: Positivity Vol. 18, no. 1 (2014), p. 171-189
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- 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 examined. In particular, we establish the equivalence of one of these constraint qualifications with the recently suggested by Andreani et al. Constant rank of the subspace component constraint qualification. As an application, we make use of this new constraint qualification in the local analysis of the solution map to a parameterized equilibrium problem, modeled by a generalized equation.
Quantitative characterizations of regularity properties of collections of sets
- Authors: Kruger, Alexander , Thao, Nguyen
- Date: 2015
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 164, no. 1 (2015), p. 41-67
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- 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 of sets and those of set-valued mappings are provided.
Some new characterizations of intrinsic transversality in hilbert spaces
- Authors: Thao, Nguyen , Bui, Hoa , Cuong, Nguyen , Verhaegen, Michel
- Date: 2020
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 28, no. 1 (2020), p. 5-39
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- Description: Motivated by a number of questions concerning transversality-type properties of pairs of sets recently raised by Ioffe and Kruger, this paper reports several new characterizations of the intrinsic transversality property in Hilbert spaces. New results in terms of normal vectors clarify the picture of intrinsic transversality, its variants and sufficient conditions for subtransversality, and unify several of them. For the first time, intrinsic transversality is characterized by an equivalent condition which does not involve normal vectors. This characterization offers another perspective on intrinsic transversality. As a consequence, the obtained results allow us to answer a number of important questions about transversality-type properties. © 2020, The Author(s).
New Farkas-type results for vector-valued functions : A non-abstract approach
- Authors: Dinh, Nguyen , Goberna, Miguel , Long, Dang , Lopez-Cerda, Marco
- Date: 2019
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 182, no. 1 (2019), p. 4-29
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- Description: This paper provides new Farkas-type results characterizing the inclusion of a given set, called contained set, into a second given set, called container set, both of them are subsets of some locally convex space, called decision space. The contained and the container sets are described here by means of vector functions from the decision space to other two locally convex spaces which are equipped with the partial ordering associated with given convex cones. These new Farkas lemmas are obtained via the complete characterization of the conic epigraphs of certain conjugate mappings which constitute the core of our approach. In contrast with a previous paper of three of the authors (Dinh et al. in J Optim Theory Appl 173:357-390, 2017), the aimed characterizations of the containment are expressed here in terms of the data.
Aggregate subgradient method for nonsmooth DC optimization
- Authors: Bagirov, Adil , Taheri, Sona , Joki, Kaisa , Karmitsa, Napsu , Mäkelä, Marko
- Date: 2021
- Type: Text , Journal article
- Relation: Optimization Letters Vol. 15, no. 1 (2021), p. 83-96
- Relation: http://purl.org/au-research/grants/arc/DP190100580
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- Description: The aggregate subgradient method is developed for solving unconstrained nonsmooth difference of convex (DC) optimization problems. The proposed method shares some similarities with both the subgradient and the bundle methods. Aggregate subgradients are defined as a convex combination of subgradients computed at null steps between two serious steps. At each iteration search directions are found using only two subgradients: the aggregate subgradient and a subgradient computed at the current null step. It is proved that the proposed method converges to a critical point of the DC optimization problem and also that the number of null steps between two serious steps is finite. The new method is tested using some academic test problems and compared with several other nonsmooth DC optimization solvers. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
Facially exposed cones are not always nice
- Authors: Roshchina, Vera
- Date: 2014
- Type: Text , Journal article
- Relation: SIAM Journal on Optimization Vol. 24, no. 1 (2014), p. 257-268
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- Description: We address the conjecture proposed by Gábor Pataki that every facially exposed cone is nice. We show that the conjecture is true in the three-dimensional case; however, there exists a four-dimensional counterexample of a cone that is facially exposed but is not nice.
A counterexample to De Pierro's conjecture on the convergence of under-relaxed cyclic projections
- Authors: Cominetti, Roberto , Roshchina, Vera , Williamson, Andrew
- Date: 2019
- Type: Text , Journal article
- Relation: Optimization Vol. 68, no. 1 (2019), p. 3-12
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- Description: The convex feasibility problem consists in finding a point in the intersection of a finite family of closed convex sets. When the intersection is empty, a best compromise is to search for a point that minimizes the sum of the squared distances to the sets. In 2001, de Pierro conjectured that the limit cycles generated by the ε-under-relaxed cyclic projection method converge when ε ↓ 0 towards a least squares solution. While the conjecture has been confirmed under fairly general conditions, we show that it is false in general by constructing a system of three compact convex sets in R3 for which the ε-under-relaxed cycles do not converge. © 2018 Informa UK Limited, trading as Taylor & Francis Group.
Optimization of parameters of the Kelvin element in vibration analysis
- Authors: Kuznetsov, Alexey , Mammadov, Musa , Hajilarov, Eldar
- Date: 2009
- Type: Text , Conference paper
- Relation: Paper presented at 2009 IEEE International Conference on Industrial Technology, ICIT 2009, Churchill, VIC January 2009
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- Description: In this paper we consider the problem of finding optimal parameters of the Kelvin element in vibration analysis. This problem is based on finding analytical solution of the initial ODE for development of the optimization model. Such technique allows us to compute optimal parameters of Kelvin element.
A fuzzy derivative and dynamical systems
- Authors: Mammadov, Musa
- Date: 2002
- Type: Text , Thesis , PhD
- Full Text:
- Description: "The purpose of this thesis is to develop and study new techniques for the mathematical modeling of dynamical systems and to apply these techniques to data classification problems. This approach is based on the notion of a fuzzy derivative. The main aim of the thesis is to examine this notion in data classification."
- Description: Doctor of Philosophy