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Dual-stage adaptive finite-time modified function projective multi-lag combined synchronization for multiple uncertain chaotic systems

Qiaoping LiSanyang Liu — 2017

Open Mathematics

In this paper, for multiple different chaotic systems with unknown bounded disturbances and fully unknown parameters, a more general synchronization method called modified function projective multi-lag combined synchronization is proposed. This new method covers almost all of the synchronization methods available. As an advantage of the new method, the drive system is a linear combination of multiple chaotic systems, which makes the signal hidden channels more abundant and the signal hidden methods...

A class of extensions of Restricted (s,t)-Wythoff’s game

Sanyang LiuHaiyan Li — 2017

Open Mathematics

Restricted (s, t)-Wythoff’s game, introduced by Liu et al. in 2014, is an impartial combinatorial game. We define and solve a class of games obtained from Restricted (s, t)-Wythoff’s game by adjoining to it some subsets of its P-positions as additional moves. The results show that under certain conditions they are equivalent to one case in which only one P-position is adjoined as an additional move. Furthermore, two winning strategies of exponential and polynomial are provided for the games.

A smoothing Levenberg-Marquardt method for the complementarity problem over symmetric cone

Xiangjing LiuSanyang Liu — 2022

Applications of Mathematics

In this paper, we propose a smoothing Levenberg-Marquardt method for the symmetric cone complementarity problem. Based on a smoothing function, we turn this problem into a system of nonlinear equations and then solve the equations by the method proposed. Under the condition of Lipschitz continuity of the Jacobian matrix and local error bound, the new method is proved to be globally convergent and locally superlinearly/quadratically convergent. Numerical experiments are also employed to show that...

A new branch and bound algorithm for minimax ratios problems

Yingfeng ZhaoSanyang LiuHongwei Jiao — 2017

Open Mathematics

This study presents an efficient branch and bound algorithm for globally solving the minimax fractional programming problem (MFP). By introducing an auxiliary variable, an equivalent problem is firstly constructed and the convex relaxation programming problem is then established by utilizing convexity and concavity of functions in the problem. Other than usual branch and bound algorithm, an adapted partition skill and a practical reduction technique performed only in an unidimensional interval are...

Outcome space range reduction method for global optimization of sum of affine ratios problem

Hongwei JiaoSanyang LiuJingben YinYingfeng Zhao — 2016

Open Mathematics

Many algorithms for globally solving sum of affine ratios problem (SAR) are based on equivalent problem and branch-and-bound framework. Since the exhaustiveness of branching rule leads to a significant increase in the computational burden for solving the equivalent problem. In this study, a new range reduction method for outcome space of the denominator is presented for globally solving the sum of affine ratios problem (SAR). The proposed range reduction method offers a possibility to delete a large...

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