In this paper, a new formulation of three-dimensional spherical discontinuous deformation analysis (DDA) based on second-order cone programming has been proposed. Artificial springs with open-close iteration used in c...
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In this paper, a new formulation of three-dimensional spherical discontinuous deformation analysis (DDA) based on second-order cone programming has been proposed. Artificial springs with open-close iteration used in classic DDA have been removed, given that improper stiffness parameters might cause numerical problems. Furthermore, to account for irregular granular shapes, a rolling resistance model is incorporated in the variational formulation. The proposed formulation can be cast into a standard second-order cone programming program, which can be solved using efficient off-the-shelf optimisation solvers. The proposed approach is validated by a series of numerical examples.
Selecting the relevant factors in a particular domain is of utmost interest in the machine learning community. This paper concerns the feature selection process for twin support vector machine (TWSVM), a powerful clas...
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Selecting the relevant factors in a particular domain is of utmost interest in the machine learning community. This paper concerns the feature selection process for twin support vector machine (TWSVM), a powerful classification method that constructs two nonparallel hyperplanes in order to define a classification rule. Besides the Euclidean norm, our proposal includes a second regularizer that aims at eliminating variables in both twin hyperplanes in a synchronized fashion. The baseline classifier is a twin SVM implementation based on secondorderconeprogramming, which confers robustness to the approach and leads to potentially better predictive performance compared to the standard TWSVM formulation. The proposal is studied empirically and compared with well-known feature selection methods using microarray datasets, on which it succeeds at finding low dimensional solutions with highest average performance among all the other methods studied in this work.
In this paper, we consider a continuous version of the convex network flow problem which involves the integral of the Euclidean norm of the flow and its square in the objective function. A discretized version of this ...
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In this paper, we consider a continuous version of the convex network flow problem which involves the integral of the Euclidean norm of the flow and its square in the objective function. A discretized version of this problem can be cast as a second-ordercone program, for which efficient primal-dual interior-point algorithms have been developed recently. An optimal magnetic shielding design problem of the MAGLEV train, a new bullet train under development in Japan, is formulated as the continuous convex network flow problem and is solved with the primal-dual interior-point algorithm. Taking advantage of its efficiency and stability, we further apply the algorithm to robust design of the magnetic shielding.
Feature selection is an important machine learning topic, especially in high dimensional applications, such as cancer prediction with microarray data. This work addresses the issue of high dimensionality of feature se...
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Feature selection is an important machine learning topic, especially in high dimensional applications, such as cancer prediction with microarray data. This work addresses the issue of high dimensionality of feature selection for linear and kernel-based Support Vector Machines (SVMs) considering second-order cone programming formulations. These formulations provide a robust and efficient framework for classification, while an adequate feature selection process avoids errors in the estimation of means and covariances. Our approach is based on a sequential backward elimination which uses different linear and kernel-based contribution measures to determine the feature relevance. Experimental results with microarray datasets demonstrate the effectiveness in terms of predictive performance and construction of a low-dimensional data representation.
The maximum-crossrange problem is an optimal control problem of computing the maximum crossrange reachable by a hypersonic entry vehicle at a specified downrange, which has long known to be very difficult to solve due...
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The maximum-crossrange problem is an optimal control problem of computing the maximum crossrange reachable by a hypersonic entry vehicle at a specified downrange, which has long known to be very difficult to solve due to its high nonlinearities and non-convexity. This paper presents how to convexify the problem so that it can be efficiently solved by successive second-order cone programming (SOCP). Particular focus is given on equivalent transformation of the original optimization objective and rigorous establishment of validity of the relaxation process used for convexification. In addition, it is observed that iteratively solving the SOCP problems may not always guarantee convergence to the original problem, a simple line search approach is proposed which is found critical to ensure the convergence of the successive SOCP method. Numerical demonstrations are provided to illustrate the effectiveness and efficiency of the proposed method and its applicability to both orbital and suborbital missions. (C) 2015 Elsevier Masson SAS. All rights reserved.
second-order cone programming (SOCP) problems are typically solved by interior point methods. As in linear programming (LP), interior point methods can, in theory, solve SOCPs in polynomial time and can, in practice, ...
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second-order cone programming (SOCP) problems are typically solved by interior point methods. As in linear programming (LP), interior point methods can, in theory, solve SOCPs in polynomial time and can, in practice, exploit sparsity in the problem data. Specifically, when cones of large dimension are present, the density that results in the normal equations that are solved at each iteration can be remedied in a manner similar to the treatment of dense columns in an LP. Here we propose a product-form Cholesky factorization (PFCF) approach, and show that it is more numerically stable than the alternative Sherman-Morrison-Woodbury approach. We derive several PFCF variants and compare their theoretical performance. Finally, we prove that the elements of L in the Cholesky factorizations LDLT that arise in interior point methods for SOCP are uniformly bounded as the duality gap tends to zero as long as the iterates remain is some conic neighborhood of the cental path.
The meshless element-free Galerkin (EFG) method is extended to allow computation of the limit load of plates. A kinematic formulation that involves approximating the displacement field using the moving least-squares t...
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The meshless element-free Galerkin (EFG) method is extended to allow computation of the limit load of plates. A kinematic formulation that involves approximating the displacement field using the moving least-squares technique is developed. Only one displacement variable is required for each EFG node, ensuring that the total number of variables in the resulting optimization problem is kept to a minimum, with far fewer variables being required compared with finite element formulations using compatible elements. A stabilized conforming nodal integration scheme is extended to plastic plate bending problems. The evaluation of integrals at nodal points using curvature smoothing stabilization both keeps the size of the optimization problem small and also results in stable and accurate solutions. Difficulties imposing essential boundary conditions are overcome by enforcing displacements at the nodes directly. The formulation can be expressed as the problem of minimizing a sum of Euclidean norms subject to a set of equality constraints. This non-smooth minimization problem can be transformed into a form suitable for solution using second-order cone programming. The procedure is applied to several benchmark beam and plate problems and is found in practice to generate good upper-bound solutions for benchmark problems. Copyright (C) 2009 John Wiley & Sons, Ltd.
Frame structures are extensively used in mechanical, civil, and aerospace engineering. Besides generating reasonable designs of frame structures themselves, frame topology optimization may serve as a tool providing us...
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Frame structures are extensively used in mechanical, civil, and aerospace engineering. Besides generating reasonable designs of frame structures themselves, frame topology optimization may serve as a tool providing us with conceptual designs of diverse engineering structures. Due to its nonconvexity, however, most of existing approaches to frame topology optimization are local optimization methods based on nonlinear programming with continuous design variables or (meta)heuristics allowing some discrete design variables. Presented in this paper is a new global optimization approach to the frame topology optimization with discrete design variables. It is shown that the compliance minimization problem with predetermined candidate cross-sections can be formulated as a mixed-integer second-order cone programming problem. The global optimal solution is then computed with an existing solver based on a branch-and-cut algorithm. Numerical experiments are performed to examine computational efficiency of the proposed approach.
A new formulation is presented for equilibrium shape analysis of cable networks considering geometrical and material non-linearities. Friction between cables and joint devices is also considered. The second-ordercone...
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A new formulation is presented for equilibrium shape analysis of cable networks considering geometrical and material non-linearities. Friction between cables and joint devices is also considered. The second-order cone programming (SOCP) problem which has the same solution as that of minimization of total potential energy is solved to obtain the equilibrium configuration. The optimality conditions are derived to verify that the solution satisfies equilibrium conditions and friction laws. Since no assumption on stress state is needed in the proposed method, no process of trial and error is involved. No effort is required to develop any analysis software because SOCP can be solved by using the well-developed software based on the interior-point method. Copyright (C) 2002 John Wiley Sons, Ltd.
In design practice it is often that the structural components are selected from among easily available discrete candidates and a number of different candidates used in a structure is restricted to be small. Presented ...
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In design practice it is often that the structural components are selected from among easily available discrete candidates and a number of different candidates used in a structure is restricted to be small. Presented in this paper is a new modeling of the design constraints for obtaining the minimum compliance truss design in which only a limited number of different cross-section sizes are employed. The member cross-sectional areas are considered either discrete design variables that can take only predetermined values or continuous design variables. In both cases it is shown that the compliance minimization problem can be formulated as a mixed-integer second-order cone programming problem. The global optimal solution of this optimization problem is then computed by using an existing solver based on a branch-and-cut algorithm. Numerical experiments are performed to show that the proposed approach is applicable to moderately large-scale problems.
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