Spline function smooth support vector machine for classification

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TR Number

Date

2007-08

Journal Title

Journal ISSN

Volume Title

Publisher

American Institute of Mathematical Sciences

Abstract

This paper presents a duality theory for solving concave minimization problem and nonconvex quadratic programming problem subjected to nonlinear inequality constraints. By use of the canonical dual transformation developed recently, two canonical dual problems are formulated, respectively. These two dual problems are perfectly dual to the primal problems with zero duality gap. It is proved that the sufficient conditions for global minimizers and local extrema (both minima and maxima) are controlled by the triality theory discovered recently [5]. This triality theory can be used to develop certain useful primal-dual methods for solving difficult nonconvex minimization problems. Results shown that the difficult quadratic minimization problem with quadratic constraint can be converted into a one-dimensional dual problem, which can be solved completely to obtain all KKT points and global minimizer.

Description

Keywords

global optimization, duality, concave minimization, quadratic, programming, np-hard problems, optimality condition, engineering, multidisciplinary, operations research & management, science, mathematics, interdisciplinary applications

Citation

Yuan, Y. B.; Fan, W. G.; Pu, D. M., "Spline function smooth support vector machine for classification," J. Industrial and Management Optimization 3(3), 529-542, (2007); DOI: 10.3934/jimo.2007.3.529