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4Miller, Mirka
3Gao, David
3Rubinov, Alex
2Lin, Yuqing
2Ruan, Ning
2Sugeng, Kiki Ariyanti
1Balbuena, Camino
1Barker, Ewan
1Chen, Yi
1Das, K. C.
1Fang, Shucherng
1Gasimov, Rafail
1Lawton, Alan
1López, Marco
1Marti, J. Gomez
1Martinez-Legaz, Juan
1Petschel, Helen
1Rodger, Chris
1Rogers, Pauline
1Ryan, Joe

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4Graph theory
4Integer programming
30102 Applied Mathematics
30802 Computation Theory and Mathematics
3Canonical duality theories
3Convex set
3Functions
3Global optimization
3Theorem proving
20101 Pure Mathematics
20103 Numerical and Computational Mathematics
2Canonical duality
2Computational complexity
2Duality
2Integer optimization
2Maximization problem
2Optimization
2Optimization techniques
2Problem solving

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Ordinal number in a prep classroom

- Petschel, Helen, Rogers, Pauline

**Authors:**Petschel, Helen , Rogers, Pauline**Date:**2006**Type:**Text , Journal article**Relation:**Prime Number Vol. 21, no. 4 (2006), p. 28-29**Full Text:**false**Description:**The focus of the lesson was ordinal number. The students were rotated through three activities in a team teaching environment. These activities were: the construction of towers with building blocks, toy cars in a garage and racing plastic animals. The activity involving the racing of the plastic animals gave an interesting result that sparked discussion between the staff. The following article presents the activity, what happened and a reflection of why we thought this result occurred.

An efficient classification using support vector machines

- Ruan, Ning, Chen, Yi, Gao, David

**Authors:**Ruan, Ning , Chen, Yi , Gao, David**Date:**2013**Type:**Text , Conference paper**Relation:**Proceedings of 2013 Science and Information Conference, SAI 2013 p. 585-589**Full Text:**false**Reviewed:****Description:**Support vector machine (SVM) is a popular method for classification in data mining. The canonical duality theory provides a unified analytic solution to a wide range of discrete and continuous problems in global optimization. This paper presents a canonical duality approach for solving support vector machine problem. It is shown that by the canonical duality, these nonconvex and integer optimization problems are equivalent to a unified concave maximization problem over a convex set and hence can be solved efficiently by existing optimization techniques. © 2013 The Science and Information Organization.

All (k;g)-cages are k-edge-connected

- Lin, Yuqing, Miller, Mirka, Rodger, Chris

**Authors:**Lin, Yuqing , Miller, Mirka , Rodger, Chris**Date:**2005**Type:**Text , Journal article**Relation:**Journal of Graph Theory Vol. 48, no. 3 (2005), p. 219-227**Full Text:**false**Reviewed:****Description:**A (k;g)-cage is a k-regular graph with girth g and with the least possible number of vertices. In this paper, we prove that (k;g)-cages are k-edge-connected if g is even. Earlier, Wang, Xu, and Wang proved that (k;g)-cages are k-edge-connected if g is odd. Combining our results, we conclude that the (k;g)-cages are k-edge-connected. © 2005 wiley Periodicals, Inc.**Description:**C1

- Rubinov, Alex, Gasimov, Rafail

**Authors:**Rubinov, Alex , Gasimov, Rafail**Date:**2004**Type:**Text , Journal article**Relation:**Journal of Global Optimization Vol. 29, no. 4 (2004), p. 455-477**Full Text:**false**Reviewed:****Description:**We consider problems of vector optimization with preferences that are not necessarily a pre-order relation. We introduce the class of functions which can serve for a scalarization of these problems and consider a scalar duality based on recently developed methods for non-linear penalization scalar problems with a single constraint.**Description:**C1**Description:**2003000932

On the degrees of a strongly vertex-magic graph

- Balbuena, Camino, Barker, Ewan, Das, K. C., Lin, Yuqing, Miller, Mirka, Ryan, Joe, Slamin,, Sugeng, Kiki Ariyanti, Tkac, M.

**Authors:**Balbuena, Camino , Barker, Ewan , Das, K. C. , Lin, Yuqing , Miller, Mirka , Ryan, Joe , Slamin, , Sugeng, Kiki Ariyanti , Tkac, M.**Date:**2006**Type:**Text , Journal article**Relation:**Discrete Mathematics Vol. 306, no. 6 (2006), p. 539-551**Full Text:**false**Reviewed:****Description:**Let G=(V,E) be a finite graph, where |V|=n≥2 and |E|=e≥1. A vertex-magic total labeling is a bijection λ from V∪E to the set of consecutive integers {1,2,...,n+e} with the property that for every v∈V, λ(v)+∑w∈N(v)λ(vw)=h for some constant h. Such a labeling is strong if λ(V)={1,2,...,n}. In this paper, we prove first that the minimum degree of a strongly vertex-magic graph is at least two. Next, we show that if 2e≥10n2-6n+1, then the minimum degree of a strongly vertex-magic graph is at least three. Further, we obtain upper and lower bounds of any vertex degree in terms of n and e. As a consequence we show that a strongly vertex-magic graph is maximally edge-connected and hamiltonian if the number of edges is large enough. Finally, we prove that semi-regular bipartite graphs are not strongly vertex-magic graphs, and we provide strongly vertex-magic total labeling of certain families of circulant graphs. © 2006 Elsevier B.V. All rights reserved**Description:**C1**Description:**2003001603

On consecutive edge magic total labeling of graphs

- Sugeng, Kiki Ariyanti, Miller, Mirka

**Authors:**Sugeng, Kiki Ariyanti , Miller, Mirka**Date:**2008**Type:**Text , Journal article**Relation:**Journal of Discrete Algorithms Vol. 6, no. 1 (2008), p. 59-65**Full Text:**false**Reviewed:****Description:**Let G = (V, E) be a finite (non-empty) graph, where V and E are the sets of vertices and edges of G. An edge magic total labeling is a bijection**Description:**C1

Two new families of large compound graphs

- Marti, J. Gomez, Miller, Mirka

**Authors:**Marti, J. Gomez , Miller, Mirka**Date:**2006**Type:**Text , Journal article**Relation:**Networks Vol. 47, no. 3 (2006), p. 140-146**Full Text:**false**Reviewed:****Description:**A question of special interest in graph theory is the design of large graphs. Specifically, we want to find constructions of graphs with order as large as possible for a given degree A and diameter D. Two generalizations of two large compound graphs are proposed in this article. Three particular cases of these families of graphs presented here allow us to improve the order for the entries (15, 7), (13, 10), and (15, 10) in the table of the largest known (Δ, D)-graphs. © 2006 Wiley Periodicals, Inc.**Description:**C1**Description:**2003001599

Increasing quasiconcave co-radiant functions with applications in mathematical economics

- Martinez-Legaz, Juan, Rubinov, Alex, Schaible, Siegfried

**Authors:**Martinez-Legaz, Juan , Rubinov, Alex , Schaible, Siegfried**Date:**2005**Type:**Text , Journal article**Relation:**Mathematical Methods of Operations Research Vol. 61, no. 2 (2005), p. 261-280**Full Text:**false**Reviewed:****Description:**We study increasing quasiconcave functions which are co-radiant. Such functions have frequently been employed in microeconomic analysis. The study is carried out in the contemporary framework of abstract convexity and abstract concavity. Various properties of these functions are derived. In particular we identify a small "natural" infimal generator of the set of all coradiant quasiconcave increasing functions. We use this generator to examine two duality schemes for these functions: classical duality often used in microeconomic analysis and a more recent duality concept. Some possible applications to the theory of production functions and utility functions are discussed. © Springer-Verlag 2005.**Description:**C1**Description:**2003001423

Towards a theory of integrity systems: a configurational approach

- Six, Frederique, Lawton, Alan

**Authors:**Six, Frederique , Lawton, Alan**Date:**2013**Type:**Text , Journal article**Relation:**International Review of Administrative Sciences Vol. 79, no. 4 (2013), p. 639-658**Full Text:**false**Reviewed:****Description:**The integrity of public officials is considered a key determinant of public trust in government and a central concept in good governance. An integrity system consists of all components, such as policies, practices, institutions and integrity guardians meant to contribute to the integrity of the organization at the heart of the integrity system. In this article we propose a theoretical model for the effectiveness of integrity systems that can be tested empirically. Six conditions are proposed as important for delivering the outcome of high integrity performance. Different configurations are expected to deliver the same outcome, because of varying developmental trajectories. Implications for further research are discussed. Points for practitioners Many countries have in place measures for dealing with corruption and unethical behaviour on the part of public officials. Rarely are these measures considered as part of a whole system. At the same time, there is little research evidence for the effectiveness of individual measures or the system as a whole. This article addresses these issues and is, therefore, important for policy makers who are developing anti-corruption measures.

- Yuan, Y. B., Fang, Shucherng, Gao, David

**Authors:**Yuan, Y. B. , Fang, Shucherng , Gao, David**Date:**2012**Type:**Text , Journal article**Relation:**Journal of Global Optimization Vol. 52, no. 2 (2012), p. 195-209**Full Text:**false**Reviewed:****Description:**This paper studies the canonical duality theory for solving a class of quadri- nomial minimization problems subject to one general quadratic constraint. It is shown that the nonconvex primal problem in Rn can be converted into a concave maximization dual problem over a convex set in R2 , such that the problem can be solved more efficiently. The existence and uniqueness theorems of global minimizers are provided using the triality theory. Examples are given to illustrate the results obtained. © 2011 Springer Science+Business Media, LLC.

Canonical duality theory and algorithm for solving challenging problems in network optimisation

**Authors:**Ruan, Ning , Gao, David**Date:**2012**Type:**Text , Conference paper**Relation:**19th International Conference on Neural Information Processing, ICONIP 2012 Vol. 7665 LNCS, p. 702-709**Full Text:****Reviewed:****Description:**This paper presents a canonical dual approach for solving a general nonconvex problem in network optimization. Three challenging problems, sensor network location, traveling salesman problem, and scheduling problem are listed to illustrate the applications of the proposed method. It is shown that by the canonical duality, these nonconvex and integer optimization problems are equivalent to unified concave maximization problem over a convex set and hence can be solved efficiently by existing optimization techniques. © 2012 Springer-Verlag.**Description:**2003010653

**Authors:**Ruan, Ning , Gao, David**Date:**2012**Type:**Text , Conference paper**Relation:**19th International Conference on Neural Information Processing, ICONIP 2012 Vol. 7665 LNCS, p. 702-709**Full Text:****Reviewed:****Description:**This paper presents a canonical dual approach for solving a general nonconvex problem in network optimization. Three challenging problems, sensor network location, traveling salesman problem, and scheduling problem are listed to illustrate the applications of the proposed method. It is shown that by the canonical duality, these nonconvex and integer optimization problems are equivalent to unified concave maximization problem over a convex set and hence can be solved efficiently by existing optimization techniques. © 2012 Springer-Verlag.**Description:**2003010653

Stability of the lower level sets of ICAR functions

- López, Marco, Rubinov, Alex, Vera De Serio, Virginia

**Authors:**López, Marco , Rubinov, Alex , Vera De Serio, Virginia**Date:**2005**Type:**Text , Journal article**Relation:**Numerical Functional Analysis and Optimization Vol. 26, no. 1 (2005), p. 113-127**Full Text:**false**Reviewed:****Description:**In this paper, we study the stability of the lower level set {x E R++n | f (x) ≤ 0} of a finite valued increasing convex-along-rays (ICAR) function f defined on R++n. In monotonic analysis, ICAR functions play the role of usual convex functions in classical convex analysis. We show that each ICAR function f is locally Lipschitz on int dom f and that the pointwise convergence of a sequence of ICAR functions implies its uniform convergence on each compact subset of R ++n. The latter allows us to establish stability results for ICAR functions in some sense similar to those for convex functions. Copyright © Taylor & Francis, Inc.**Description:**C1**Description:**2003001419

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