Stability solution definite quadratic programs

Belousov, E. Bonnans, J. Springer, New York Dontchev, A. Eaves, B. Gauvin, J. Study 19 , — Lee, G. Google Scholar. Global Optim. Theory Appl. Luo, Z. Cambridge University Press, Cambridge Robinson, S. Study 10 , — Rockafellar, R. By Theorems 3. In the case of , Figure 2 reveals that the projection neural network 2. In the case of , Figure 3 reveals that the projection neural network 2. These are in accordance with the conclusion of Theorems 3. In the case of , Figure 4 reveals that the projection neural network 2.

In the case of , Figure 5 reveals that the projection neural network 2. In this paper, we have developed a new projection neural network for solving interval quadratic programs, the equilibrium point of the proposed neural network is equivalent to the solution of interval quadratic programs. A condition is derived which ensures the existence, uniqueness, and global exponential stability of the equilibrium point. The results obtained are highly valuable in both theory and practice for solving interval quadratic programs in engineering.

This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article of the Year Award: Outstanding research contributions of , as selected by our Chief Editors.

Read the winning articles. Journal overview. Special Issues. Academic Editor: Jitao Sun. Received 26 Feb Accepted 19 Jul Published 29 Aug Abstract This paper presents a nonlinear projection neural network for solving interval quadratic programs subject to box-set constraints in engineering applications.

Introduction In lots of engineering applications including regression analysis, image and signal progressing, parameter estimation, filter design and robust control, and so forth [ 1 ], it is necessary to solve the following quadratic programming problem: where , , and is a convex set.

A Projection Neural Network Model Consider the following interval quadratic programming problem: where , , ; , and is a positive definite diagonal matrix. Figure 1. Architecture of the proposed neural network in 2.

Figure 2. Convergence of the state trajectory of the neural network with random initial value 2. Figure 3. Convergence of the state trajectory of the neural network with random initial value - 2. Figure 4. Convergence of the state trajectory of the neural network with random initial value - 0.

Figure 5. Convergence of the state trajectory of the neural network with random initial value 0. References M. Bazaraa, H. Sherali, and C. Kennedy and L. Xia and J. Xia, G. Feng, and J. Xia and G. Yang and J. Tao, J. Cao, and D. Xue and W. Tuy, H. Springer International Publishing AG Global Optim. Ye, Y. In: Recent Advances in Global Optimization, 19— Princeton University Press Yuan, Y. Download references. The authors would like to thank the referee and the Handling Editor for their valuable comments and kind suggestions.

You can also search for this author in PubMed Google Scholar. Correspondence to Nguyen Huy Chieu. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Reprints and Permissions. Acta Math Vietnam 45, — Download citation. Received : 22 August Revised : 26 April Accepted : 06 May Published : 19 June Issue Date : June Anyone you share the following link with will be able to read this content:. Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative. Skip to main content. Search SpringerLink Search. Abstract This paper examines tilt stability for quadratic programs with one or two quadratic inequality constraints.

References 1.