Mcplib: a collection of nonlinear mixed complementarity problems

Dirkse, Steven P.; Ferris, Michael C.

doi:10.1080/10556789508805619

Cited by 259 publications

(173 citation statements)

References 22 publications

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“…For each complementarity model, we only solved the first linear system arising from (3). The termination criteria for these tests was based upon the relative residual, " °\\${x0)\\-• ^e iterative methods terminated when the relative residual is less than 10" 8 When using the GMRES method, we need to choose the restart frequency. We varied the value of m by choosing values between 10 and 200.…”

Section: Discussionmentioning

confidence: 99%

“…To test the standard algorithm, we ran the code on all of the problems in the GAMSLIB and MCPLIB [8] suites of test problems. All of the models in GAMSLIB were solved and are not reported here.…”

Section: Restartingmentioning

confidence: 99%

“…Issues related to the use of iterative solvers for large scale problems are outlined. We demonstrate the code's robustness on the problems in the MCPLIB [8] test collection by performing two tests, one using direct solution methods and another using only iterative techniques. Both indicate that the code is reliable and scalable.…”

Section: Introductionmentioning

confidence: 99%

“…Any new algorithmic development should attempt to meet the expectations of the modeling community; the resulting code must terminate in all cases with appropriate solutions or error messages, and should solve a vast majority of the standard suite of test models [8].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Semismooth Algorithm for Large Scale Complementarity Problems

Munson

Facchinei²,

Ferris³

et al. 2001

INFORMS Journal on Computing

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Complementarity solvers are continually being challenged by modelers demanding improved reliability and scalability. Building upon a strong theoretical background, the semismooth algorithm has the potential to meet both of these requirements. We briefly discuss relevant theory associated with the algorithm and describe a sophisticated implementation in detail. Particular emphasis is given to robust methods for dealing with singularities in the linear system and to large scale issues. Results on the MCPLIB test suite indicate that the code is robust and has the potential to solve very large problems.

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Section: Discussionmentioning

confidence: 99%

Section: Restartingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Semismooth Algorithm for Large Scale Complementarity Problems

Munson

Facchinei²,

Ferris³

et al. 2001

INFORMS Journal on Computing

Self Cite

View full text Add to dashboard Cite

show abstract

“…Let S denote the solution set of problem (1). Throughout this paper, we assume that S is nonempty and F has the property that (2) F (y), y − x * ≥ 0 for all y ∈ C and all x * ∈ S, where ·, · denotes the usual inner product in R n .…”

Section: Introductionmentioning

confidence: 99%

A New Projection Algorithm for Solving a System of Nonlinear Equations With Convex Constraints

Lian¹

2013

Bulletin of the Korean Mathematical Society

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Abstract. We present a new algorithm for solving a system of nonlinear equations with convex constraints which combines proximal point and projection methodologies. Compared with the existing projection methods for solving the problem, we use a different system of linear equations to obtain the proximal point; and moreover, at the step of getting next iterate, our projection way and projection region are also different. Based on the Armijo-type line search procedure, a new hyperplane is introduced. Using the separate property of hyperplane, the new algorithm is proved to be globally convergent under much weaker assumptions than monotone or more generally pseudomonotone. We study the convergence rate of the iterative sequence under very mild error bound conditions.

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Another hybrid approach for solving monotone operator equations and application to signal processing

Abubakar

Ibrahim

Kura³

et al. 2022

Math Methods in App Sciences

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This paper presents a hybrid conjugate gradient (CG) approach for solving nonlinear equations and signal reconstruction. The CG parameter of the approach is a convex combination of the Dai‐Yuan (DY)‐like and Hestenes‐Stiefel (HS)‐like parameters. Independent of any line search, the search direction is descent and bounded. Under some reasonable assumptions, the global convergence of the hybrid approach is proved. Numerical experiments on some benchmark test problems show that the proposed approach is efficient compared with some existing algorithms. Finally, the proposed approach is applied in signal reconstruction.

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Mcplib: a collection of nonlinear mixed complementarity problems

Cited by 259 publications

References 22 publications

The Semismooth Algorithm for Large Scale Complementarity Problems

The Semismooth Algorithm for Large Scale Complementarity Problems

A New Projection Algorithm for Solving a System of Nonlinear Equations With Convex Constraints

Another hybrid approach for solving monotone operator equations and application to signal processing

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