A Full-Newton Step Infeasible Interior-Point Method for the Special Weighted Linear Complementarity Problem

Chi, Xiaoni; Wang, Guoqiang

doi:10.1007/s10957-021-01873-4

Cited by 13 publications

(3 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Throughout this paper, we assume that the special wLCP (1) satisfies the interior point condition (IPC), i. e., F 0 ¹ AE, which implies the existence of a solution for the problem (1). Since A is a matrix supposed full row rank and the IPC holds, the parameter system (2) has a unique solution for each 0 < t ≤ t 0 [18] . It is denoted as (x(t)y(t)s(t)) and we call it the t-center of the special wLCP (1).…”

Section: Full-newton Step Primal-dual Interior-point Algorithmmentioning

confidence: 99%

A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function

GENG,

ZHANG,

ZHU

2024

Wuhan Univ. J. Nat. Sci.

View full text Add to dashboard Cite

In this paper, a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed. The algorithm employs a kernel function with a linear growth term to derive the search direction, and by introducing new technical results and selecting suitable parameters, we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods. Furthermore, numerical results illustrate the efficiency of the proposed method.

show abstract

Section: Full-newton Step Primal-dual Interior-point Algorithmmentioning

confidence: 99%

A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function

GENG,

ZHANG,

ZHU

2024

Wuhan Univ. J. Nat. Sci.

View full text Add to dashboard Cite

show abstract

“…Gowda [10] discussed a class of WLCP over Euclidean Jordan algebra. Chi et al [11,12] proposed infeasible interior-point methods for WLCPs, which have good computational complexity. Asadi et al [13] presented a modified interior-point method and obtained an iteration bound for the monotone WLCP.…”

Section: Introductionmentioning

confidence: 99%

Strong Convergence of a Two-Step Modified Newton Method for Weighted Complementarity Problems

Liu

Zhang

2023

Axioms

View full text Add to dashboard Cite

This paper focuses on the weighted complementarity problem (WCP), which is widely used in the fields of economics, sciences and engineering. Not least because of its local superlinear convergence rate, smoothing Newton methods have widespread application in solving various optimization problems. A two-step smoothing Newton method with strong convergence is proposed. With a smoothing complementary function, the WCP is reformulated as a smoothing set of equations and solved by the proposed two-step smoothing Newton method. In each iteration, the new method computes the Newton equation twice, but using the same Jacobian, which can avoid consuming a lot of time in the calculation. To ensure the global convergence, a derivative-free line search rule is inserted. At the same time, we develop a different term in the solution of the smoothing Newton equation, which guarantees the local strong convergence. Under appropriate conditions, the algorithm has at least quadratic or even cubic local convergence. Numerical experiments indicate the stability and effectiveness of the new method. Moreover, compared to the general smoothing Newton method, the two-step smoothing Newton method can significantly improve the computational efficiency without increasing the computational cost.

show abstract

“…When w = 0, the WCP (2) becomes the NCP [4][5][6]. When the function G(x, y, u) becomes linear, then the WCP (2) is reduced to (1) [7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

A Two-Step Newton Algorithm for the Weighted Complementarity Problem with Local Biquadratic Convergence

Liu,

Zhang

2023

Axioms

View full text Add to dashboard Cite

We discuss the weighted complementarity problem, extending the nonlinear complementarity problem on Rn. In contrast to the NCP, many equilibrium problems in science, engineering, and economics can be transformed into WCPs for more efficient methods. Smoothing Newton algorithms, known for their at least locally superlinear convergence properties, have been widely applied to solve WCPs. We suggest a two-step Newton approach with a local biquadratic order convergence rate to solve the WCP. The new method needs to calculate two Newton equations at each iteration. We also insert a new term, which is of crucial importance for the local biquadratic convergence properties when solving the Newton equation. We demonstrate that the solution to the WCP is the accumulation point of the iterative sequence produced by the approach. We further demonstrate that the algorithm possesses local biquadratic convergence properties. Numerical results indicate the method to be practical and efficient.

show abstract

A Full-Newton Step Infeasible Interior-Point Method for the Special Weighted Linear Complementarity Problem

Cited by 13 publications

References 27 publications

A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function

A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function

Strong Convergence of a Two-Step Modified Newton Method for Weighted Complementarity Problems

A Two-Step Newton Algorithm for the Weighted Complementarity Problem with Local Biquadratic Convergence

Contact Info

Product

Resources

About