longquan yong | Xidian University (original) (raw)

Papers by longquan yong

Modern interior point methods originated from an algorithm introduced by Karmarkar in 1984 for li... more Modern interior point methods originated from an algorithm introduced by Karmarkar in 1984 for linear programming. In the years since then, algorithms and software for linear programming have become quite popular, while extensions to more general classes of problems, such as convex quadratic programming, linear complementarity problem, semi-definite programming, second order cone programming and nonconvex and nonlinear problems, have reached varying levels of maturity. In this paper we review the interior point algorithms and applications in some optimization problems, such as linear programming, linear complementarity problem, semi-definite programming and some convex programming. Combining with the current studies, we conclude that " applications of interior point algorithms and kernel function-based interior point algorithms" will be the research focuses in the future.

A method of constructing test problems with known global solution for a class of nonlinear concav... more A method of constructing test problems with known global solution for a class of nonlinear concave and convex programs is presented. The initial polyhedron is assumed to be a hypercube; the method generates the nonlinear programs whose global solution over the given domain occurs on its edge. The reliability and efficiency of this method are demonstrated by the numerical experiments with Lingo software.

We present a new method for solving bimatrix games problems. Firstly, bimatrix games problem is t... more We present a new method for solving bimatrix games problems. Firstly, bimatrix games problem is transformed into general linear complementarity problem. Then we apply mixed integer linear programming method to linear complementarity problem. At last, we give some numerical examples to indicate that the method is feasible and effective to bimatrix games problems.

We present a new method for solving large scale nonnegative least squares problems. Firstly, nonn... more We present a new method for solving large scale nonnegative least squares problems. Firstly, nonnegative least squares problem was transformed into monotone linear complementarity problem. Then we apply potential-reduction interior point algorithm to monotone linear complementarity problem which is based on the Newton direction and centering direction. We show that this algorithm have the polynomial complexity. Numerical results are reported which demonstrate very good computational performance on nonnegative least squares problems.

Information Computing and Applications, 2011

An iterative method for solving a class of linear complementarity problems with positive definite... more An iterative method for solving a class of linear complementarity problems with positive definite symmetric matrices is presented. Firstly, linear complementarity problem is transformed into absolute value equation, which is also a fixed-point problem. Then we ...

Proceedings of the 2009 International Symposium …, 2009

We formulate the NP-hard absolute value equation as linear complementary problem when the singula... more We formulate the NP-hard absolute value equation as linear complementary problem when the singular values of A exceed one, and we proposed a mixed integer linear programming method to absolute value equation problem. The effectiveness of the method is demonstrated by its ability to solve random problems.

Artificial Intelligence and Computational Intelligence, 2010

This paper provides a survey to some of recent developments in the field of nonlinear complementa... more This paper provides a survey to some of recent developments in the field of nonlinear complementarity problems (NCP). Some existence conditions of solution to the NCP are given according to the monotonicity of the functions, and corresponding NCP examples ...

Future Computer and Communication, 2009. FCC'09. …, 2009

Abstract We study a feasible interior-point method for solving a class of nonnegative least squar... more Abstract We study a feasible interior-point method for solving a class of nonnegative least squares problems. Firstly, nonnegative least squares problem was transformed into linear complementarily problem. Then we present a feasible interior point algorithm for ...

Journal of Computational Information Systems, 2010

We investigate the NP-hard absolute value equation (AVE) Au -|u| = b, where A is an arbitrary squ... more We investigate the NP-hard absolute value equation (AVE) Au -|u| = b, where A is an arbitrary square matrix. In this paper, we present a smoothing method for the AVE. First, we replace the absolute value function by a smooth one, called aggregate function. With this smoothing technique, we formulate the non-smooth AVE as a smooth nonlinear equations, furthermore, an unconstrained differentiable optimization problem. Then we adopt Particle Swarm Optimization (PSO) to AVE. The numerical experiments show that the proposed algorithm is effective in dealing with the AVE.

academicjournals.org

A is an arbitrary square matrix whose singular values exceed one. The significance of the absolut... more A is an arbitrary square matrix whose singular values exceed one. The significance of the absolute value equations arises from the fact that linear programs, quadratic programs, bimatrix games and other problems can all be reduced to the linear complementarity problem that in turn is equivalent to the absolute value equations. In this paper, we present a smoothing method for the AVE. First, we replace the absolute value function by a smooth one, called aggregate function. With this smoothing technique, the non-smooth AVE is formulated as a smooth nonlinear equations, furthermore, an unconstrained differentiable optimization problem. Then we adopt quasi-Newton method to solve this problem. Numerical results indicate that the method is feasible and effective to absolute value equations.

Control and Decision Conference (CCDC), 2011 …, Jan 1, 2011

Abstract In last decades, there has been much effort on the solution and the analysis of the nonl... more Abstract In last decades, there has been much effort on the solution and the analysis of the nonlinear complementarity problem (NCP) by reformulating NCP as an unconstrained minimization. In this paper, we propose a new method for the NCP under the condition ...

Information and Computing …, Jan 1, 2011

Abstract A feasible interior point method is proposed for solving the NP-hard absolute value equa... more Abstract A feasible interior point method is proposed for solving the NP-hard absolute value equation (AVE) when the singular values of A exceed one. We formulate the NP-hard AVE as linear complementary problem, and prove that the solution to AVE is existent and ...

Keji Daobao/ Science & Technology Review, Jan 1, 2010

Control Conference (CCC), 2011 30th Chinese, Jan 1, 2011

Abstract Potential reduction interior point algorithm is proposed for solving the NP-hard absolut... more Abstract Potential reduction interior point algorithm is proposed for solving the NP-hard absolute value equations (AVE) Au-| u|= b. Under the condition that all the singular values of A are not less than one, the existence and uniqueness theorem of the solution to the AVE ...

Progress in Informatics and …, Jan 1, 2010

Abstract An iterative method for solving a class of nonnegative linear least squares problems is ... more Abstract An iterative method for solving a class of nonnegative linear least squares problems is presented. Firstly, nonnegative least squares problem is transformed into monotone linear complementarity problem. Then we present an iterative algorithm for monotone linear ...