Interior-point methods for nonlinear complementarity problems

Potra, Florian A.; Ye, Y.

doi:10.1007/bf02192201

Cited by 52 publications

(18 citation statements)

References 19 publications

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“…In this section we derive an algorithm for this problem based on [70]. Let us now simplify the notation and focus on the nonlinear complementarity problem in the following form:…”

Section: Interior Point Methods For Nonlinear Complementarity Problemsmentioning

confidence: 99%

Interior Point Methods for Nonlinear Optimization

Pólik

Terlaky

2010

Lecture Notes in Mathematics

297

158

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“…In this section we derive an algorithm for this problem based on [70]. Let us now simplify the notation and focus on the nonlinear complementarity problem in the following form:…”

Section: Interior Point Methods For Nonlinear Complementarity Problemsmentioning

confidence: 99%

Interior Point Methods for Nonlinear Optimization

Pólik

Terlaky

2010

Lecture Notes in Mathematics

297

158

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“…The NCP has been studied extensively due to its various applications in operations research, economics, and engineering [1,2]. Many methods have been developed to solve NCP (1.1), such as interior point methods [3,4], smoothing methods [5,6]. In this paper, we are interested in smoothing Newton methods for solving NCP (1.1).…”

Section: Introductionmentioning

confidence: 98%

“…3) In this paper, we propose and investigate a family of new smoothing functions based on p-norm with p ∈ (1, +∞). In particular, we define φ p : 3 → by φ p (μ, a, b) := (1 + μ)(a + b) − p |a + μb| p + |b + μa| p + |μ| p , ∀p ∈ (1, ∞).…”

Section: Introductionmentioning

confidence: 99%

A family of new smoothing functions and a nonmonotone smoothing Newton method for the nonlinear complementarity problems

Zhu

Liu

2010

J. Appl. Math. Comput.

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In this paper, based on a p-norm with p being any fixed real number in the interval (1, +∞), we introduce a family of new smoothing functions, which include the smoothing symmetric perturbed Fischer function as a special case. We also show that the functions have several favorable properties. Based on the new smoothing functions, we propose a nonmonotone smoothing Newton algorithm for solving nonlinear complementarity problems. The proposed algorithm only need to solve one linear system of equations. We show that the proposed algorithm is globally and locally superlinearly convergent under suitable assumptions. Numerical experiments indicate that the method associated with a smaller p, for example p = 1.1, usually has better numerical performance than the smoothing symmetric perturbed Fischer function, which exactly corresponds to p = 2.

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“…During the last few years many methods have been developed for the solution of monotone NCPs. In particular, Interior Point (IP) methods have been considered by Kojima,Noma,Yoshise [8], Potra and Ye [13], Sun and Zhao [15], Wright and Ralph [17], Tseng [18]. These algorithms follow the central path and use Newton directions on the equation of the central path.…”

Section: Introductionmentioning

confidence: 99%

An inexact interior point method for monotone NCP

Bellavia

Macconi

1999

Optimization Methods and Software

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In this paper we present an inexact Interior Point method for solving monotone nonlinear complementarity problems. We show that the theory presented by Kojima, Noma and Yoshise for an exact version of this method can be used to establish global convergence for the inexact form. Then we prove that local superlinear convergence can be achieved under some stronger hypotheses. The complexity of the algorithm is also studied under the assumption that the problem satisfies a scaled Lipschitz condition. It is proved that the feasible version of the algorithm is polynomial, while the infeasible one is globally convergent at a linear rate.

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Interior-point methods for nonlinear complementarity problems

Cited by 52 publications

References 19 publications

Interior Point Methods for Nonlinear Optimization

Interior Point Methods for Nonlinear Optimization

A family of new smoothing functions and a nonmonotone smoothing Newton method for the nonlinear complementarity problems

An inexact interior point method for monotone NCP

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