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28Bagirov, Adil
25Gao, David
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15Wu, Zhiyou
14Rubinov, Alex
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13Roshchina, Vera
13Ugon, Julien
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140913 Mechanical Engineering
120801 Artificial Intelligence and Image Processing
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Analytical solutions to general anti-plane shear problems in finite elasticity

**Authors:**Gao, David**Date:**2016**Type:**Text , Journal article**Relation:**Continuum Mechanics and Thermodynamics Vol. 28, no. 1-2 (2016), p. 175-194**Full Text:****Reviewed:****Description:**This paper presents a pure complementary energy variational method for solving a general anti-plane shear problem in finite elasticity. Based on the canonical dualityâ€“triality theory developed by the author, the nonlinear/nonconvex partial differential equations for the large deformation problem are converted into an algebraic equation in dual space, which can, in principle, be solved to obtain a complete set of stress solutions. Therefore, a general analytical solution form of the deformation is obtained subjected to a compatibility condition. Applications are illustrated by examples with both convex and nonconvex stored strain energies governed by quadratic-exponential and power-law material models, respectively. Results show that the nonconvex variational problem could have multiple solutions at each material point, the complementary gap function and the triality theory can be used to identify both global and local extremal solutions, while the popular convexity conditions (including rank-one condition) provide mainly local minimal criteria and the Legendre-Hadamard condition (i.e., the so-called strong ellipticity condition) does not guarantee uniqueness of solutions. This paper demonstrates again that the pure complementary energy principle and the triality theory play important roles in finite deformation theory and nonconvex analysis. © 2015, Springer-Verlag Berlin Heidelberg.

**Authors:**Gao, David**Date:**2016**Type:**Text , Journal article**Relation:**Continuum Mechanics and Thermodynamics Vol. 28, no. 1-2 (2016), p. 175-194**Full Text:****Reviewed:****Description:**This paper presents a pure complementary energy variational method for solving a general anti-plane shear problem in finite elasticity. Based on the canonical dualityâ€“triality theory developed by the author, the nonlinear/nonconvex partial differential equations for the large deformation problem are converted into an algebraic equation in dual space, which can, in principle, be solved to obtain a complete set of stress solutions. Therefore, a general analytical solution form of the deformation is obtained subjected to a compatibility condition. Applications are illustrated by examples with both convex and nonconvex stored strain energies governed by quadratic-exponential and power-law material models, respectively. Results show that the nonconvex variational problem could have multiple solutions at each material point, the complementary gap function and the triality theory can be used to identify both global and local extremal solutions, while the popular convexity conditions (including rank-one condition) provide mainly local minimal criteria and the Legendre-Hadamard condition (i.e., the so-called strong ellipticity condition) does not guarantee uniqueness of solutions. This paper demonstrates again that the pure complementary energy principle and the triality theory play important roles in finite deformation theory and nonconvex analysis. © 2015, Springer-Verlag Berlin Heidelberg.

Anticipating synchronization through optimal feedback control

- Huang, Tingwen, Gao, David, Li, Chuandong, Xiao, MingQing

**Authors:**Huang, Tingwen , Gao, David , Li, Chuandong , Xiao, MingQing**Date:**2012**Type:**Text , Journal article**Relation:**Journal of Global Optimization Vol. 52, no. 2 (2012), p. 281-290**Full Text:**false**Reviewed:****Description:**In this paper, we investigate the anticipating synchronization of a class of coupled chaotic systems through discontinuous feedback control. The stability criteria for the involved error dynamical system are obtained by means of model transformation incorporated with Lyapunov functional and linear matrix inequality. Also, we discuss the optimal designed controller based on the obtained criteria. The numerical simulation is presented to demonstrate the theoretical results. © 2011 Springer Science+Business Media, LLC.

Application of design structure matrix in project management

- Gunawan, Indra, Singh, Darius

**Authors:**Gunawan, Indra , Singh, Darius**Date:**2008**Type:**Text , Conference paper**Relation:**Proceedings of the 17th International Conference on Management of Technology**Full Text:**false**Reviewed:**

Application of neural network approach in construction productivity analysis

**Authors:**Gunawan, Indra**Date:**2010**Type:**Text , Journal article**Relation:**Journal of Management & Engineering Integration Vol. 10, no. 1 (2010), p. 1-11**Full Text:**false**Reviewed:**

Application of numerical design structure matrix method in engineering projects management

**Authors:**Gunawan, Indra**Date:**2009**Type:**Text , Journal article**Relation:**Operations and Supply chain Management: An International Journal Vol. 2, no. 1 (2009 2009), p. 1-10**Full Text:**false**Reviewed:****Description:**In this paper, ways of improving planning, execution and management of projects using Numerical Design Structure Matrix (NDSM) method are presented to address interdependency of feedback and iteration, which is common in engineering projects management. The NDSM is an alternative approach to traditional project management tools such as Program Evaluation and Review Technique (PERT), Critical Path Method (CPM), and Gantt chart that can only allow the modelling of sequential and parallel processes in projects. As a case study, the model is tested on a set of tasks in a complex petroleum oil field development project, where task sensitivity and information variability attributes are derived. By applying the NDSM method, project duration is optimized and hence total cost of the project is reduced significantly.

Application of numerical design structure matrix method in project management

**Authors:**Gunawan, Indra**Date:**2009**Type:**Text , Conference proceedings**Full Text:**false

Application of soft computing to predict blast-induced ground vibration

- Khandelwal, Manoj, Kumar, Lalit, Yellishetty, Mohan

**Authors:**Khandelwal, Manoj , Kumar, Lalit , Yellishetty, Mohan**Date:**2011**Type:**Text , Journal article**Relation:**Engineering with Computers Vol. 27, no. 2 (2011), p. 117-125**Full Text:**false**Reviewed:****Description:**In this study, an attempt has been made to evaluate and predict the blast-induced ground vibration by incorporating explosive charge per delay and distance from the blast face to the monitoring point using artificial neural network (ANN) technique. A three-layer feed-forward back-propagation neural network with 2-5-1 architecture was trained and tested using 130 experimental and monitored blast records from the surface coal mines of Singareni Collieries Company Limited, Kothagudem, Andhra Pradesh, India. Twenty new blast data sets were used for the validation and comparison of the peak particle velocity (PPV) by ANN and conventional vibration predictors. Results were compared based on coefficient of determination and mean absolute error between monitored and predicted values of PPV. © 2009 Springer-Verlag London Limited.

Applying the canonical dual theory in optimal control problems

- Zhu, Jinghao, Wu, Dan, Gao, David

**Authors:**Zhu, Jinghao , Wu, Dan , Gao, David**Date:**2012**Type:**Text , Journal article**Relation:**Journal of global optimization Vol. 54, no. 2 (2012), p. 221-233**Full Text:**false**Reviewed:****Description:**This paper presents some applications of the canonical dual theory in optimal control problems. The analytic solutions of several nonlinear and nonconvex problems are investigated by global optimizations. It turns out that the backward differential flow defined by the KKT equation may reach the globally optimal solution. The analytic solution to an optimal control problem is obtained via the expression of the co-state. Some examples are illustrated.

Applying UGF Concept to Enhance the Assessment Capability of FMEA

- Khorshidi, Hadi, Gunawan, Indra, Ibrahim, Yousef

**Authors:**Khorshidi, Hadi , Gunawan, Indra , Ibrahim, Yousef**Date:**2016**Type:**Text , Journal article**Relation:**Quality and Reliability Engineering International Vol. 32, no. 3 (Apr 2016), p. 1085-1093**Full Text:**false**Reviewed:****Description:**The purpose of this paper is to propose a modified version of Failure Mode and Effects Analysis (FMEA) to alleviate its drawbacks. FMEA is an important tool in risk evaluation and finding the priority of potential failure modes for corrective actions. In the proposed method, the Universal Generating Function (UGF) approach has been used to improve the assessment capability of the conventional Risk Priority Number (RPN) in ranking. The new method is named as URPN. It generates the most number of unique values in comparison with the previous methods and considers relative importance for the parameters while it is easy to compute. More unique numbers help to avoid from having the same priority level for different failure modes which represent various risk levels. A case study has been employed to demonstrate that the URPN not only can improve the shortcomings but also is able to provide accurate values for risk assessment. Copyright (c) 2015 John Wiley & Sons, Ltd.

**Authors:**Adilov, G. , Rubinov, Alex**Date:**2006**Type:**Text , Journal article**Relation:**Numerical Functional Analysis and Optimization Vol. 27, no. 3-4 (Apr-May 2006), p. 237-257**Full Text:**false**Reviewed:****Description:**A subset B of R-+(n) is B-convex if for all x, y is an element of B and all t is an element of [0, 1] one has max (tx, y) is an element of B. These sets were first investigated in [1, 2]. In this paper, we examine radiant B-convex sets and also introduce and study B-convex functions.**Description:**C1**Description:**2003001836

Best approximation in a class of normed spaces with star-shaped cone

- Mohebi, Hossein, Sadeghi, H., Rubinov, Alex

**Authors:**Mohebi, Hossein , Sadeghi, H. , Rubinov, Alex**Date:**2006**Type:**Text , Journal article**Relation:**Numerical Functional Analysis and Optimization Vol. 27, no. 3-4 (Apr-May 2006), p. 411-436**Full Text:**false**Reviewed:****Description:**We examine best approximation by closed sets in a class of normed spaces with star-shaped cones. It is assumed that the norm on the space X under consideration is generated by a star-shaped cone. First, we study best approximation by downward and upward sets, and then we use the results obtained as a tool for examination of best approximation by an arbitrary closed set.**Description:**C1**Description:**2003001837

Blast-induced ground vibration prediction using support vector machine

**Authors:**Khandelwal, Manoj**Date:**2011**Type:**Text , Journal article**Relation:**Engineering with Computers Vol. 27, no. 3 (2011), p. 193-200**Full Text:**false**Reviewed:****Description:**Ground vibrations induced by blasting are one of the fundamental problems in the mining industry and may cause severe damage to structures and plants nearby. Therefore, a vibration control study plays an important role in the minimization of environmental effects of blasting in mines. In this paper, an attempt has been made to predict the peak particle velocity using support vector machine (SVM) by taking into consideration of maximum charge per delay and distance between blast face to monitoring point. To investigate the suitability of this approach, the predictions by SVM have been compared with conventional vibration predictor equations. Coefficient of determination (CoD) and mean absolute error were taken as a performance measure. © 2010 Springer-Verlag London Limited.

Bodies with mirror surface invisible from two points

- Plakhov, Andrew, Roshchina, Vera

**Authors:**Plakhov, Andrew , Roshchina, Vera**Date:**2014**Type:**Text , Journal article**Relation:**Nonlinearity Vol. 27, no. 6 (June 2014), p. 1193-1203**Full Text:**false**Reviewed:****Description:**We consider a setting where a bounded set with a piecewise smooth boundary in Euclidean space is identified with a body with a mirror surface, and the billiard in the complement of the set is identified with the dynamics of light rays outside the body in the framework of geometric optics. We show that in this setting it is possible to construct a body invisible from two points. Â© 2014 IOP Publishing Ltd & London Mathematical Society.

Borwein-Preiss variational principle revisited

- Kruger, Alexander, Plubtieng, Somyot, Seangwattana, Thidaporn

**Authors:**Kruger, Alexander , Plubtieng, Somyot , Seangwattana, Thidaporn**Date:**2016**Type:**Text , Journal article**Relation:**Journal of Mathematical Analysis and Applications Vol. 435, no. 2 (2016), p. 1183-1193**Relation:**http://purl.org/au-research/grants/arc/DP110102011**Full Text:****Reviewed:****Description:**In this article, we refine and slightly strengthen the metric space version of the Borwein-Preiss variational principle due to Li and Shi (2000) [12], clarify the assumptions and conclusions of their Theorem 1 as well as Theorem 2.5.2 in Borwein and Zhu (2005) [4] and streamline the proofs. Our main result, Theorem 3 is formulated in the metric space setting. When reduced to Banach spaces (Corollary 9), it extends and strengthens the smooth variational principle established in Borwein and Preiss (1987) [3] along several directions. (C) 2015 Elsevier Inc. All rights reserved.

**Authors:**Kruger, Alexander , Plubtieng, Somyot , Seangwattana, Thidaporn**Date:**2016**Type:**Text , Journal article**Relation:**Journal of Mathematical Analysis and Applications Vol. 435, no. 2 (2016), p. 1183-1193**Relation:**http://purl.org/au-research/grants/arc/DP110102011**Full Text:****Reviewed:****Description:**In this article, we refine and slightly strengthen the metric space version of the Borwein-Preiss variational principle due to Li and Shi (2000) [12], clarify the assumptions and conclusions of their Theorem 1 as well as Theorem 2.5.2 in Borwein and Zhu (2005) [4] and streamline the proofs. Our main result, Theorem 3 is formulated in the metric space setting. When reduced to Banach spaces (Corollary 9), it extends and strengthens the smooth variational principle established in Borwein and Preiss (1987) [3] along several directions. (C) 2015 Elsevier Inc. All rights reserved.

Borwein–Preiss vector variational principle

- Kruger, Alexander, Plubtieng, Somyot, Seangwattana, Thidaporn

**Authors:**Kruger, Alexander , Plubtieng, Somyot , Seangwattana, Thidaporn**Date:**2017**Type:**Text , Journal article**Relation:**Positivity Vol. 21, no. 4 (2017), p. 1273-1292**Relation:**http://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**This article extends to the vector setting the results of our previous work Kruger et al. (J Math Anal Appl 435(2):1183–1193, 2016) which refined and slightly strengthened the metric space version of the Borwein–Preiss variational principle due to Li and Shi (J Math Anal Appl 246(1):308–319, 2000. doi:10.1006/jmaa.2000.6813). We introduce and characterize two seemingly new natural concepts of ε-minimality, one of them dependent on the chosen element in the ordering cone and the fixed “gauge-type” function. © 2017, Springer International Publishing.

**Authors:**Kruger, Alexander , Plubtieng, Somyot , Seangwattana, Thidaporn**Date:**2017**Type:**Text , Journal article**Relation:**Positivity Vol. 21, no. 4 (2017), p. 1273-1292**Relation:**http://purl.org/au-research/grants/arc/DP160100854**Full Text:****Reviewed:****Description:**This article extends to the vector setting the results of our previous work Kruger et al. (J Math Anal Appl 435(2):1183–1193, 2016) which refined and slightly strengthened the metric space version of the Borwein–Preiss variational principle due to Li and Shi (J Math Anal Appl 246(1):308–319, 2000. doi:10.1006/jmaa.2000.6813). We introduce and characterize two seemingly new natural concepts of ε-minimality, one of them dependent on the chosen element in the ordering cone and the fixed “gauge-type” function. © 2017, Springer International Publishing.

Calmness modulus of linear semi-infinite programs

- Cánovas, Maria, Kruger, Alexander, López, Marco, Parra, Juan, Théra, Michel

**Authors:**Cánovas, Maria , Kruger, Alexander , López, Marco , Parra, Juan , Théra, Michel**Date:**2014**Type:**Text , Journal article**Relation:**SIAM Journal on Optimization Vol. 24, no. 1 (2014), p. 29-48**Relation:**http://purl.org/au-research/grants/arc/DP110102011**Full Text:****Reviewed:****Description:**Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound on the calmness modulus for semi-infinite programs with unique optimal solution which turns out to be the exact modulus when the problem is finitely constrained. The relationship between the calmness of the argmin mapping and the same property for the (sub)level set mapping (with respect to the objective function), for semi-infinite programs and without requiring the uniqueness of the nominal solution, is explored, too, providing an upper bound on the calmness modulus of the argmin mapping. When confined to finitely constrained problems, we also provide a computable upper bound as it only relies on the nominal data and parameters, not involving elements in a neighborhood. Illustrative examples are provided.

**Authors:**Cánovas, Maria , Kruger, Alexander , López, Marco , Parra, Juan , Théra, Michel**Date:**2014**Type:**Text , Journal article**Relation:**SIAM Journal on Optimization Vol. 24, no. 1 (2014), p. 29-48**Relation:**http://purl.org/au-research/grants/arc/DP110102011**Full Text:****Reviewed:****Description:**Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound on the calmness modulus for semi-infinite programs with unique optimal solution which turns out to be the exact modulus when the problem is finitely constrained. The relationship between the calmness of the argmin mapping and the same property for the (sub)level set mapping (with respect to the objective function), for semi-infinite programs and without requiring the uniqueness of the nominal solution, is explored, too, providing an upper bound on the calmness modulus of the argmin mapping. When confined to finitely constrained problems, we also provide a computable upper bound as it only relies on the nominal data and parameters, not involving elements in a neighborhood. Illustrative examples are provided.

Calmness of partially perturbed linear systems with an application to the central path

- Cánovas, Maria, Hall, Julian, López, Marco, Parra, Juan

**Authors:**Cánovas, Maria , Hall, Julian , López, Marco , Parra, Juan**Date:**2019**Type:**Text , Journal article**Relation:**Optimization Vol. 68, no. 2-3 (2019), p. 465-483**Full Text:****Reviewed:****Description:**In this paper we develop point-based formulas for the calmness modulus of the feasible set mapping in the context of linear inequality systems with a fixed abstract constraint and (partially) perturbed linear constraints. The case of totally perturbed linear systems was previously analyzed in [Canovas MJ, Lopez MA, Parra J, et al. Calmness of the feasible set mapping for linear inequality systems. Set-Valued Var Anal. 2014;22:375-389, Section 5]. We point out that the presence of such an abstract constraint yields the current paper to appeal to a notable different methodology with respect to previous works on the calmness modulus in linear programming. The interest of this model comes from the fact that partially perturbed systems naturally appear in many applications. As an illustration, the paper includes an example related to the classical central path construction. In this example we consider a certain feasible set mapping whose calmness modulus provides a measure of the convergence of the central path. Finally, we underline the fact that the expression for the calmness modulus obtained in this paper is (conceptually) implementable as far as it only involves the nominal data.

**Authors:**Cánovas, Maria , Hall, Julian , López, Marco , Parra, Juan**Date:**2019**Type:**Text , Journal article**Relation:**Optimization Vol. 68, no. 2-3 (2019), p. 465-483**Full Text:****Reviewed:****Description:**In this paper we develop point-based formulas for the calmness modulus of the feasible set mapping in the context of linear inequality systems with a fixed abstract constraint and (partially) perturbed linear constraints. The case of totally perturbed linear systems was previously analyzed in [Canovas MJ, Lopez MA, Parra J, et al. Calmness of the feasible set mapping for linear inequality systems. Set-Valued Var Anal. 2014;22:375-389, Section 5]. We point out that the presence of such an abstract constraint yields the current paper to appeal to a notable different methodology with respect to previous works on the calmness modulus in linear programming. The interest of this model comes from the fact that partially perturbed systems naturally appear in many applications. As an illustration, the paper includes an example related to the classical central path construction. In this example we consider a certain feasible set mapping whose calmness modulus provides a measure of the convergence of the central path. Finally, we underline the fact that the expression for the calmness modulus obtained in this paper is (conceptually) implementable as far as it only involves the nominal data.

Canonical dual least square method for solving general nonlinear systems of quadratic equations

**Authors:**Ruan, Ning , Gao, David**Date:**2010**Type:**Text , Journal article**Relation:**Computational Optimization and Applications Vol. 47, no. (2010), p. 335-347**Full Text:**false**Reviewed:****Description:**This paper presents a canonical dual approach for solving general non- linear algebraic systems. By using least square method, the nonlinear system of m -quadratic equations in n -dimensional space is first formulated as a nonconvex opti- mization problem. We then proved that, by the canonical duality theory developed by the second author, this nonconvex problem is equivalent to a concave maximization problem in R, which can be solved easily by well-developed convex optimization techniques. Both existence and uniqueness of global optimal solutions are discussed, and several illustrative examples are presented.**Description:**C1

Canonical duality for solving general nonconvex constrained problems

- Latorre, Vittorio, Gao, David

**Authors:**Latorre, Vittorio , Gao, David**Date:**2016**Type:**Text , Journal article**Relation:**Optimization Letters Vol. 10, no. 8 (2016), p. 1763-1779**Full Text:****Reviewed:****Description:**This paper presents a canonical duality theory for solving a general nonconvex constrained optimization problem within a unified framework to cover Lagrange multiplier method and KKT theory. It is proved that if both target function and constraints possess certain patterns necessary for modeling real systems, a perfect dual problem (without duality gap) can be obtained in a unified form with global optimality conditions provided.While the popular augmented Lagrangian method may produce more difficult nonconvex problems due to the nonlinearity of constraints. Some fundamental concepts such as the objectivity and Lagrangian in nonlinear programming are addressed.

**Authors:**Latorre, Vittorio , Gao, David**Date:**2016**Type:**Text , Journal article**Relation:**Optimization Letters Vol. 10, no. 8 (2016), p. 1763-1779**Full Text:****Reviewed:****Description:**This paper presents a canonical duality theory for solving a general nonconvex constrained optimization problem within a unified framework to cover Lagrange multiplier method and KKT theory. It is proved that if both target function and constraints possess certain patterns necessary for modeling real systems, a perfect dual problem (without duality gap) can be obtained in a unified form with global optimality conditions provided.While the popular augmented Lagrangian method may produce more difficult nonconvex problems due to the nonlinearity of constraints. Some fundamental concepts such as the objectivity and Lagrangian in nonlinear programming are addressed.

Canonical duality theory and triality for solving general global optimization problems in complex systems

- Morales-Silva, Daniel, Gao, David

**Authors:**Morales-Silva, Daniel , Gao, David**Date:**2015**Type:**Text , Journal article**Relation:**Mathematics and Mechanics of Complex Systems Vol. 3, no. 2 (2015), p. 139-161**Full Text:****Reviewed:****Description:**General nonconvex optimization problems are studied by using the canonical duality-triality theory. The triality theory is proved for sums of exponentials and quartic polynomials, which solved an open problem left in 2003. This theory can be used to find the global minimum and local extrema, which bridges a gap between global optimization and nonconvex mechanics. Detailed applications are illustrated by several examples. © 2015 Mathematical Sciences Publishers.

**Authors:**Morales-Silva, Daniel , Gao, David**Date:**2015**Type:**Text , Journal article**Relation:**Mathematics and Mechanics of Complex Systems Vol. 3, no. 2 (2015), p. 139-161**Full Text:****Reviewed:****Description:**General nonconvex optimization problems are studied by using the canonical duality-triality theory. The triality theory is proved for sums of exponentials and quartic polynomials, which solved an open problem left in 2003. This theory can be used to find the global minimum and local extrema, which bridges a gap between global optimization and nonconvex mechanics. Detailed applications are illustrated by several examples. © 2015 Mathematical Sciences Publishers.

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