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Preface: Special issue of JOGO MEC EurOPT 2010-Izmir

Primal necessary characterizations of transversality properties

  • Authors: Cuong, Nguyen , Kruger, Alexander
  • Date: 2021
  • Type: Text , Journal article
  • Relation: Positivity Vol. 25, no. 2 (2021), p. 531-558
  • Relation: http://purl.org/au-research/grants/arc/DP160100854
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  • Description: This paper continues the study of general nonlinear transversality properties of collections of sets and focuses on primal necessary (in some cases also sufficient) characterizations of the properties. We formulate geometric, metric and slope characterizations, particularly in the convex setting. The Hölder case is given a special attention. Quantitative relations between the nonlinear transversality properties of collections of sets and the corresponding regularity properties of set-valued mappings as well as two nonlinear transversality properties of a convex set-valued mapping to a convex set in the range space are discussed. © 2020, Springer Nature Switzerland AG.

Quadratic form representations via generalized continuants

  • Authors: Delorme, Charles , Pineda-Villavicencio, Guillermo
  • Date: 2015
  • Type: Text , Journal article
  • Relation: Journal of Integer Sequences Vol. 18, no. 6 (2015), p. Article number 15.6.4
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  • Description: H. J. S. Smith proved Fermat’s two-square theorem using the notion of palindromic continuants. In this paper we extend Smith’s approach to proper binary quadratic form representations in some commutative Euclidean rings, including rings of integers and rings of polynomials over fields of odd characteristic. Also, we present new deterministic algorithms for finding the corresponding proper representations. © 2015 University of Waterloo. All rights reserved.

Quantitative characterizations of regularity properties of collections of sets

Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems

  • Authors: Cánovas, Maria , López, Marco , Mordukhovich, Borris , Parra, Juan
  • Date: 2012
  • Type: Text , Journal article
  • Relation: TOP Vol. 20, no. 2 (2012), p. 310-327
  • Relation: http://purl.org/au-research/grants/arc/DP110102011
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  • Description: The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel-Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system's data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504-1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system's coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.

Quasistatic thermoviscoelastic problem with normal compliance, multivalued friction and wear diffusion

  • Authors: Gasi , Ochal, Anna , Shillor, Meir
  • Date: 2016
  • Type: Text , Journal article
  • Relation: Nonlinear Analysis: Real World Applications Vol. 27, no. (2016), p. 183-202
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  • Description: This paper presents and analyzes a model for quasistatic frictional contact between a thermoviscoelastic body and a moving foundation that involves wear of the contacting surface and the diffusion of the wear debris. The constitutive law includes temperature effects and the evolution of the temperature is described by a parabolic equation with a subdifferential heat exchange boundary condition. Contact is modeled with normal compliance together with a subdifferential frictional law. The rate of wear of the contact surface is described by the differential form of the Archard condition. The effects of the diffusion of the wear particles on the contact surface are taken into account. Such situations arise in mechanical joints and in orthopedic biomechanics where the wear debris is trapped, diffuses and influences the properties of joint prosthesis and implants. The variational formulation of the problem leads to a system with a time-dependent hemivariational inequality for the displacement, a parabolic hemivariational inequality for the temperature and a parabolic equation on the contact boundary for the wear diffusion. The existence of a unique weak solution is proved by using recent results from the theory of hemivariational inequalities, variational diffusion equation, and a fixed point argument. © 2015 Elsevier Ltd.

Reachability and controllability of linear switched impulsive systems

  • Authors: Liu, Chao , Han, Qi , Li, Chuandong , Zhang, Qun
  • Date: 2013
  • Type: Text , Journal article
  • Relation: IET Control Theory and Applications Vol. 7, no. 9 (2013), p. 1294-1299
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  • Description: This study investigates the reachability and controllability of linear switched impulsive systems in which impulsive component is independent of switching among different subsystems. Some crucial geometrical criteria are established. The authors present the fact that the reachable sets and the controllable sets may not be subspaces, if impulsive matrices are singular. While impulsive matrices are reversible, the reachable and controllable subspaces can be determined by two proposed subspace algorithms. The authors also point out that the reachable or controllable subspace is an invariant subspace of the considered systems. Finally, two simple corresponding examples are discussed to illustrate the correctness and effectiveness of the proposed theoretical results. © The Institution of Engineering and Technology 2013.
  • Description: C1

Real-time localisation system for GPS-denied open areas using smart street furniture

  • Authors: Nassar, Mohamed , Luxford, Len , Cole, Peter , Oatley, Giles , Koutsakis, Polychronis
  • Date: 2021
  • Type: Text , Journal article
  • Relation: Simulation Modelling Practice and Theory Vol. 112, no. (2021), p.
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  • Description: Wifi-based localisation systems have gained significant interest with many researchers proposing different localisation techniques using publicly available datasets. However, these datasets are limited because they only contain Wifi fingerprints collected and labelled by users, and they are restricted to indoor locations. We have generated the first Wifi-based localisation datasets for a GPS-denied open area. We selected a busy open area at Murdoch University to generate the datasets using so-called “smart bins”, which are rubbish bins that we enabled to work as access points. The data gathered consists of two different datasets. In the first, four users generated labelled WiFi fingerprints for all available Reference Points using four different smartphones. The second dataset includes 2450865 auto-generated rows received from more than 1000 devices. We have developed a light-weight algorithm to label the second dataset from the first and we proposed a localisation approach that converts the second dataset from asynchronous format to synchronous, applies feature engineering and a deep learning classifier. Finally, we have demonstrated via simulations that by using this approach we achieve higher prediction accuracy, with up to 19% average improvement, compared with using only the fingerprint dataset. © 2021 Elsevier B.V.

Recent contributions to linear semi-infinite optimization

Redundant paths and reliability bounds in gamma networks

  • Authors: Gunawan, Indra
  • Date: 2008
  • Type: Text , Journal article
  • Relation: Applied Mathematical modelling Vol. 32, no. (2008 2008), p. 588-594
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  • Description: Multistage Interconnection Networks (MINs) are network systems providing fast and efficient communications at a reasonable cost. A gamma network is a specific class of MINs, which provides redundant paths in the system. In a gamma network, information from source nodes is transmitted through a specific set of routes to destination nodes. Reliability of an MIN is used as a measure of system’s ability to transform information from input to output devices. Due to the complexity of network configuration and availability of redundant paths, reliability bounds to estimate the exact reliability of a gamma network is proposed. A numerical example of an 8 × 8 gamma network is presented to demonstrate the accuracy of the reliability bounds. When the lower bound reliability provides sufficient assurance that the system will be operational at some specified time and closely approximates the exact reliability, then no further effort for obtaining the exact reliability expression is necessary.

Refining the partition for multifold conic optimization problems

  • Authors: Ramirez, Hector , Roshchina, Vera
  • Date: 2020
  • Type: Text , Journal article
  • Relation: Optimization Vol. 69, no. 11 (2020), p. 2489-2507
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  • Description: In this paper, we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in Bonnans and Ramirez [Perturbation analysis of second-order cone programming problems, Math Program. 2005;104(2-30):205-227] for conic optimization problems, and in Pena and Roshchina [A complementarity partition theorem for multifold conic systems, Math Program. 2013;142(1-2):579-589] for homogeneous feasibility problems. We show that both can be treated within the same unified geometric framework and extend the latter notion to optimization problems. We also show that the two partitions do not coincide, and their intersection gives a seven-set index partition. Finally, we demonstrate that the partitions are preserved under the application of nonsingular linear transformations, and in particular, that a standard conversion of a second-order cone program into a semidefinite programming problem preserves the partitions.
  • Description: This research was partially supported by ANID (Chile) under REDES project number 180032 and by the Australian Research Council grant DE150100240. The second author was supported by FONDECYT (Fondo de Fomento al Desarrollo Cientifico y Tecnologico) regular projects 1160204 and 1201982, and Basal Program CMM-AFB 170001 (Comision Nacional de Investigacion Cientifica y Tecnologica), all from ANID (Chile).

Robust modelling of implicit interfaces by the scaled boundary finite element method

  • Authors: Dsouza, Shaima , Pramod, A. L. N. , Ooi, Ean Tat , Song, Chongming , Natarajan, Sundararajan
  • Date: 2021
  • Type: Text , Journal article
  • Relation: Engineering Analysis with Boundary Elements Vol. 124, no. (2021), p. 266-286
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  • Description: In this paper, we propose a robust framework based on the scaled boundary finite element method to model implicit interfaces in two-dimensional differential equations in nonhomegeneous media. The salient features of the proposed work are: (a) interfaces can be implicitly defined and need not conform to the background mesh; (b) Dirichlet boundary conditions can be imposed directly along the interface; (c) does not require special numerical integration technique to compute the bilinear and the linear forms and (d) can work with an efficient local mesh refinement using hierarchical background meshes. Numerical examples involving straight interface, circular interface and moving interface problems are solved to validate the proposed technique. Further, the presented technique is compared with conforming finite element method in terms of accuracy and convergence. From the numerical studies, it is seen that the proposed framework yields solutions whose error is O(h2) in L2 norm and O(h) in the H1 semi-norm. Further the condition number increases with the mesh size similar to the FEM. © 2021 Elsevier Ltd

ROI engine : return on investment model for the implementation of maintenance best practices

Second-order variational analysis in conic programming with applications to optimality and stability

  • Authors: Mordukhovich, Boris , Outrata, Jiri , Ramírez, Hector
  • Date: 2015
  • Type: Text , Journal article
  • Relation: SIAM Journal on Optimization Vol. 25, no. 1 (2015), p. 76-101
  • Relation: http://purl.org/au-research/grants/arc/DP110102011
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  • 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 differential approach of variational analysis to calculate appropriate derivatives and coderivatives of the corresponding solution maps. These developments allow us to resolve some important issues related to conic programming. They include verifiable conditions for isolated calmness of the considered solution maps, sharp necessary optimality conditions for a class of mathematical programs with equilibrium constraints, and characterizations of tilt-stable local minimizers for cone-constrained problems. The main results obtained in the general conic programming setting are specified for and illustrated by the second-order cone programming. © 2015 Society for Industrial and Applied Mathematics.

Separation properties via connectedness of topological convexity spaces

  • Authors: Sharikov, Evgeny
  • Date: 2010
  • Type: Text , Journal article
  • Relation: Pacific Journal of Optimization Vol. 6, no. 2, Suppl. 1 (2010), p. 227-241
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  • Description: For a given collection H of subsets of a set X we examine the convexity on X generated by H. We use a special type of connectedness of H and X for investigation of separation of convex sets by elements of H. In particular, we give a description of convex sets, which can be represented as the intersection of a subfamily of H. As an application, we give a description of abstract convex functions and sets. We also describe the abstract convex hull of a finite union of abstract convex sets.

Set regularities and feasibility problems

Shape optimization in contact problems with Coulomb friction and a solution-dependent friction coefficient

  • Authors: Beremlijski, Petr , Haslinger, Jaroslav , Outrata, Jiri , Pathó, Róbert
  • Date: 2014
  • Type: Text , Journal article
  • Relation: SIAM Journal on Control and Optimization Vol. 52, no. 5 (2014), p. 3371-3400
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  • Description: The present paper deals with shape optimization in discretized two-dimensional (2D) contact problems with Coulomb friction, where the coefficient of friction is assumed to depend on the unknown solution. Discretization of the continuous state problem leads to a system of finite-dimensional implicit variational inequalities, parametrized by the so-called design variable, that determines the shape of the underlying domain. It is shown that if the coefficient of friction is Lipschitz and sufficiently small in the C0,1 -norm, then the discrete state problems are uniquely solvable for all admissible values of the design variable (the admissible set is assumed to be compact), and the state variables are Lipschitzian functions of the design variable. This facilitates the numerical solution of the discretized shape optimization problem by the so-called implicit programming approach. Our main results concern sensitivity analysis, which is based on the well-developed generalized differential calculus of B. Mordukhovich and generalizes some of the results obtained in this context so far. The derived subgradient information is then combined with the bundle trust method to compute several model examples, demonstrating the applicability and efficiency of the presented approach. © 2014 Society for Industrial and Applied Mathematics

Sigma supporting cone and optimality conditions in non-convex problems

  • Authors: Hassani, Sara , Mammadov, Musa
  • Date: 2014
  • Type: Text , Journal article
  • Relation: Far East Journal of Mathematical Sciences Vol. 91, no. 2 (2014), p. 169-190
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  • Description: In this paper, a new supporting function for characterizing non-convex sets is introduced. The notions of σ-supporting cone and maximal conic gap are proposed and some properties are investigated. By applying these new notions, we establish the optimality conditions considered in [7] for a broader class of finite dimensional normed spaces in terms of weak subdifferentials.

Solutions to quadratic minimization problems with box and integer constraints

Solving DC programs using the cutting angle method