Local convergence of interior-point algorithms for degenerate monotone LCP

Monteiro, Renato D. C.; Wright, Stephen J.

doi:10.1007/bf01300971

Cited by 55 publications

(28 citation statements)

References 9 publications

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“…Using Lemma 1, the fundamental paper of Monteiro and Wright [15], and the techniques used in the proof of Theorem 1 of Mizuno [13], we obtain the following result.…”

Section: Lemmamentioning

confidence: 92%

Q-superlinear convergence of the iterates in primal-dual interior-point methods

Potra

2001

Math. Program.

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Abstract. Sufficient conditions are given for the Q-superlinear convergence of the iterates produced by primal-dual interior-point methods for linear complementarity problems. It is shown that those conditions are satisfied by several well known interior-point methods. In particular it is shown that the iteration sequences produced by the simplified predictor-corrector method of Gonzaga and Tapia, the simplified largest step method of Gonzaga and Bonnans, the LPF+ algorithm of Wright, the higher order methods of Wright and Zhang, Potra and Sheng, and Stoer, Wechs and Mizuno are Q-superlinearly convergent.

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“…Using Lemma 1, the fundamental paper of Monteiro and Wright [15], and the techniques used in the proof of Theorem 1 of Mizuno [13], we obtain the following result.…”

Section: Lemmamentioning

confidence: 92%

Q-superlinear convergence of the iterates in primal-dual interior-point methods

Potra

2001

Math. Program.

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“…In this case we say that our HLCP is nondegenerate. As mentioned in the introduction this assumption is not restrictive, since according to [11] strict complementarity is a necessary condition for superlinear convergence for a large class of interior point methods using only first order derivatives.…”

Section: Theorem 32 If Hlcp (21) Is Monotone Then Algorithm 1 Is Wementioning

confidence: 99%

“…Subsequently Ye and Anstreicher [19] proved that MTY converges quadratically assuming only that the LCP is nondegenerate. The nondegeneracy assumption is not restrictive, since according to [11] a large class of interior point methods, which contains MTY, can have only linear convergence if this assumption is violated. However as shown in [15,16] it is possible to obtain superlinear convergence even in the degenerate case by using higher order predictors.…”

Section: Introductionmentioning

confidence: 99%

On the Local Convergence of a Predictor-Corrector Method for Semidefinite Programming

Ji¹,

Potra²,

Sheng³

1999

SIAM J. Optim.

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“…As mentioned before a large class of first order interior point methods cannot have superlinear convergence without this assumption [24]. In order to obtain superlinear convergence for degenerate LCP's one has to either use nonstandard interior point methods or to consider higher order methods.…”

mentioning

confidence: 99%

“…Subsequently, Ye and Anstreicher [50] proved that MTY converges quadratically assuming only that the LCP is nondegenerate. The nondegeneracy assumption is not restrictive, since according to [24] a large class of interior point methods, which contains MTY, can have only linear convergence if this assumption is violated.…”

mentioning

confidence: 99%

Primal-Dual Affine Scaling Interior Point Methods for Linear Complementarity Problems

Potra¹

2008

SIAM J. Optim.

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Abstract. A first order affine scaling method and two mth order affine scaling methods for solving monotone linear complementarity problems (LCP) are presented. All three methods produce iterates in a wide neighborhood of the central path. The first order method has O(nL 2 (log nL 2 )(log log nL 2 )) iteration complexity. If the LCP admits a strict complementary solution then both the duality gap and the iteration sequence converge superlinearly with Q-order two. If m = Ω(log( √ nL)), then both higher order methods have O( √ n)L iteration complexity. The Q-order of convergence of one of the methods is (m + 1) for problems that admit a strict complementarity solution while the Q-order of convergence of the other method is (m + 1)/2 for general monotone LCPs.

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Local convergence of interior-point algorithms for degenerate monotone LCP

Cited by 55 publications

References 9 publications

Q-superlinear convergence of the iterates in primal-dual interior-point methods

Q-superlinear convergence of the iterates in primal-dual interior-point methods

On the Local Convergence of a Predictor-Corrector Method for Semidefinite Programming

Primal-Dual Affine Scaling Interior Point Methods for Linear Complementarity Problems

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