In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional d...In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113（2008）, 283-298] to constrained optimization problems.展开更多
The Kuhn-Tucker theorem in nondifferential form is a well-known classical optimality criterion for a convex programming problems which is true for a convex problem in the case when a Kuhn-Tucker vector exists. It is n...The Kuhn-Tucker theorem in nondifferential form is a well-known classical optimality criterion for a convex programming problems which is true for a convex problem in the case when a Kuhn-Tucker vector exists. It is natural to extract two features connected with the classical theorem. The first of them consists in its possible “impracticability” (the Kuhn-Tucker vector does not exist). The second feature is connected with possible “instability” of the classical theorem with respect to the errors in the initial data. The article deals with the so-called regularized Kuhn-Tucker theorem in nondifferential sequential form which contains its classical analogue. A proof of the regularized theorem is based on the dual regularization method. This theorem is an assertion without regularity assumptions in terms of minimizing sequences about possibility of approximation of the solution of the convex programming problem by minimizers of its regular Lagrangian, that are constructively generated by means of the dual regularization method. The major distinctive property of the regularized Kuhn-Tucker theorem consists that it is free from two lacks of its classical analogue specified above. The last circumstance opens possibilities of its application for solving various ill-posed problems of optimization, optimal control, inverse problems.展开更多
Support vector machine (SVM) technique has recently become a research focus in intrusion detection field for its better generalization performance when given less priori knowledge than other soft-computing techniques....Support vector machine (SVM) technique has recently become a research focus in intrusion detection field for its better generalization performance when given less priori knowledge than other soft-computing techniques. But the randomicity of parameter selection in its implement often prevents it achieving expected performance. By utilizing genetic algorithm (GA) to optimize the parameters in data preprocessing and the training model of SVM simultaneously, a hybrid optimization algorithm is proposed in the paper to address this problem. The experimental results demonstrate that it’s an effective method and can improve the performance of SVM-based intrusion detection system further.展开更多
基金The Graduate Students Innovate Scientific Research Program (YJSCX2008-158HLJ) of Heilongjiang Provincesupported by the Distinguished Young Scholar Foundation (JC200707) of Heilongjiang Province of China
文摘In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113（2008）, 283-298] to constrained optimization problems.
文摘The Kuhn-Tucker theorem in nondifferential form is a well-known classical optimality criterion for a convex programming problems which is true for a convex problem in the case when a Kuhn-Tucker vector exists. It is natural to extract two features connected with the classical theorem. The first of them consists in its possible “impracticability” (the Kuhn-Tucker vector does not exist). The second feature is connected with possible “instability” of the classical theorem with respect to the errors in the initial data. The article deals with the so-called regularized Kuhn-Tucker theorem in nondifferential sequential form which contains its classical analogue. A proof of the regularized theorem is based on the dual regularization method. This theorem is an assertion without regularity assumptions in terms of minimizing sequences about possibility of approximation of the solution of the convex programming problem by minimizers of its regular Lagrangian, that are constructively generated by means of the dual regularization method. The major distinctive property of the regularized Kuhn-Tucker theorem consists that it is free from two lacks of its classical analogue specified above. The last circumstance opens possibilities of its application for solving various ill-posed problems of optimization, optimal control, inverse problems.
基金This work was supported by the Research Grant of SEC E-Institute :Shanghai High Institution Grid and the Science Foundation ofShanghai Municipal Commission of Science and Technology No.00JC14052
文摘Support vector machine (SVM) technique has recently become a research focus in intrusion detection field for its better generalization performance when given less priori knowledge than other soft-computing techniques. But the randomicity of parameter selection in its implement often prevents it achieving expected performance. By utilizing genetic algorithm (GA) to optimize the parameters in data preprocessing and the training model of SVM simultaneously, a hybrid optimization algorithm is proposed in the paper to address this problem. The experimental results demonstrate that it’s an effective method and can improve the performance of SVM-based intrusion detection system further.
