There recently has been much interest in smoothing-type algorithms for solving the linear second-orderconeprogramming (LSOCP). We extend such method to solve the convex second-order cone programming (CSOCP), which i...
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There recently has been much interest in smoothing-type algorithms for solving the linear second-orderconeprogramming (LSOCP). We extend such method to solve the convex second-order cone programming (CSOCP), which is an extension of the LSOCP. In this paper, we first propose a new smoothing function. Based on this function, we establish a smoothing Newton algorithm for solving the CSOCP and prove that the algorithm is globally and locally quadratically convergent under suitable assumptions. For the established algorithm, we use a generalized Armijo-type search rule to generate the step size. Some numerical results are reported which indicate the effectiveness of our algorithm.
In this paper, we present a measure of distance in a second-ordercone based on a class of continuously differentiable strictly convex functions on R(++). Since the distance function has some favorable properties simi...
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In this paper, we present a measure of distance in a second-ordercone based on a class of continuously differentiable strictly convex functions on R(++). Since the distance function has some favorable properties similar to those of the D-function (Censor and Zenios in J. Optim. Theory Appl. 73:451-464 [1992]), we refer to it as a quasi D-function. Then, a proximal-like algorithm using the quasi D-function is proposed and applied to the second-coneprogramming problem, which is to minimize a closed proper convex function with general second-ordercone constraints. Like the proximal point algorithm using the D-function (Censor and Zenios in J. Optim. Theory Appl. 73:451-464 [1992];Chen and Teboulle in SIAM J. Optim. 3:538-543 [1993]), under some mild assumptions we establish the global convergence of the algorithm expressed in terms of function values;we show that the sequence generated by the proposed algorithm is bounded and that every accumulation point is a solution to the considered problem.
Recently, some kinds of extensions of the binary support vector machine (SVM) to multiclass classification have been proposed. In this paper, we focus on the multiobjective multiclass support vector machine based on t...
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ISBN:
(纸本)9781424496365
Recently, some kinds of extensions of the binary support vector machine (SVM) to multiclass classification have been proposed. In this paper, we focus on the multiobjective multiclass support vector machine based on the one-against-all method (MMSVM-OA), which is an improved new model from one-against-all and all-together methods. The model finds a weighted combination of binary SVMs obtained by the one-against-all method whose weights are determined in order to maximize geometric margins of its multiclass discriminant function for the generalization ability similarly to the all-together method. In addition, the model does not require a large amount of computational resources, while it is reported that it outperforms than one-against-all and all-together methods in numerical experiments. However, it is not formulated as a quadratic programming problem unlike to standard SVMs, it is difficult to apply the kernel method to it. Therefore, in this paper, we propose a nonlinear model derived by a transformation of the MMSVM-OA, which the kernel method can apply to, and show the corresponding multiclass classifier is obtained by solving a convex second-order cone programming problem. Moreover, we show the advantage of the proposed model through numerical experiments.
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