A new finitely convergent algorithm for systems of nonlinear inequalities

Jian, Jinbao; Zhang, Xue-Lu; Quan, Ran

doi:10.1016/j.aml.2006.05.007

Cited by 7 publications

(3 citation statements)

References 5 publications

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“…When they are linear ones, the simple linear programming algorithms can be used. When the inequalities (6) are nonlinear ones, the existing method in [9] could solve the nonlinear inequalities (6).…”

Section: Robust Stabilizing Controller Designmentioning

confidence: 99%

Robust Stabilizing Controller Design for the Uncertain Discrete-Time Linear Switching Systems

Fan

2013

2013 Third International Conference on Instrumentation, Measurement, Computer, Communication and Control

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This paper discussed the discrete-time linear switching systems whose discrete mode transitions are caused by discrete disturbance events and have continuous state reset functions, in the presence of parameter uncertainty state and control input bounds, the problem of robust stabilizing controller design is researched, and a method of static state feedback stabilizing controller is proposed. The relation between robust stability and existence of a robust controlled invariant set is constructed, and a test condition which can achieve in finite number steps is given. Based on the robust stability condition and the notation of linear un-saturation region for control input, the proposed robust stabilizing controller can be obtained by solving of a finite number of inequalities. At last, a numerical example is given to show the validity of the method.

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Section: Robust Stabilizing Controller Designmentioning

confidence: 99%

Robust Stabilizing Controller Design for the Uncertain Discrete-Time Linear Switching Systems

Fan

2013

2013 Third International Conference on Instrumentation, Measurement, Computer, Communication and Control

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“…Therefore, if any two spheres have overlapping orthogonal projection onto the line l, which must satisfy the following formula: (2) represents nonlinear inequalities with two variables. At present, optimization methods are usually used to solve multivariate nonlinear inequalities [10] . Solved by using optimization methods, Formula (2) needs to be transformed, that is: cos cos sin cos sin 0 cos cos sin cos sin 0…”

Section: ) the Calculation Process Of Op Detectionmentioning

confidence: 99%

Robustness analysis for three-dimensional node localization in wireless sensor networks

Liu

Dong

Song

2015

2015 21st Asia-Pacific Conference on Communications (APCC)

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Node flip ambiguity is a key problem that needs to be addressed for range-based node localization in wireless sensor networks. In this paper we have implemented robustness analysis for three-dimensional node localization in wireless sensor networks. A robustness criterion to detect flip ambiguity for range-based three-dimensional nodes localization is proposed. We have proposed that flip ambiguity detection for threedimensional node localization is equal to whether there is a plane intersecting with all range error spheres of the reference nodes of the unknown node, which is called the existence of intersecting plane (EIP) problem. To solve EIP problem, we further have proposed two solving algorithms: common tangent plane algorithm (CTP) and orthogonal projection algorithm (OP). The simulation experiments demonstrate that CTP has good detection results, but its computational complexity is too high; however, OP has almost the same detection results as CTP and has lower computational complexity.

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“…On the other hand, since the solution methods for systems of nonlinear inequalities (SNI) play important role in constrained optimization and other subjects, many methods for solving SNI were presented, see e.g., [15][16][17][18][19]. Recently, Jian, Cheng and Ke [19] proposed a finitely convergent algorithm for SNI, that is, the algorithm can produce a solution after a finite number of iterations.…”

Section: Introductionmentioning

confidence: 99%

A new ɛ-generalized projection method of strongly sub-feasible directions for inequality constrained optimization

Jian

Guo

2011

J Syst Sci Complex

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In this paper, the nonlinear optimization problems with inequality constraints are discussed. Combining the ideas of the strongly sub-feasible directions method and the ε-generalized projection technique, a new algorithm starting with an arbitrary initial iteration point for the discussed problems is presented. At each iteration, the search direction is generated by a new ε-generalized projection explicit formula, and the step length is yielded by a new Armijo line search. Under some necessary assumptions, not only the algorithm possesses global and strong convergence, but also the iterative points always get into the feasible set after finite iterations. Finally, some preliminary numerical results are reported.

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A new finitely convergent algorithm for systems of nonlinear inequalities

Cited by 7 publications

References 5 publications

Robust Stabilizing Controller Design for the Uncertain Discrete-Time Linear Switching Systems

Robust Stabilizing Controller Design for the Uncertain Discrete-Time Linear Switching Systems

Robustness analysis for three-dimensional node localization in wireless sensor networks

A new ɛ-generalized projection method of strongly sub-feasible directions for inequality constrained optimization

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