Complementarity problems

Billups, Stephen C.; Murty, Katta G.

doi:10.1016/s0377-0427(00)00432-5

Cited by 104 publications

(60 citation statements)

References 4 publications

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“…The Linear Complementarity Problem (3) arises in many contexts and has stimulated considerable research [10] [11]. One method of solving LCPs involves the use of a so-called NCP function φ(·, ·) whose root satisfies the complementarity condition…”

Section: B Smoothing Methods For Lcpsmentioning

confidence: 99%

Stochastic Complementarity for Local Control of Discontinuous Dynamics

Tassa

Todorov

2010

Robotics: Science and Systems VI

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Abstract-We present a method for smoothing discontinuous dynamics involving contact and friction, thereby facilitating the use of local optimization techniques for control. The method replaces the standard Linear Complementarity Problem with a Stochastic Linear Complementarity Problem. The resulting dynamics are continuously differentiable, and the resulting controllers are robust to disturbances. We demonstrate our method on a simulated 6-dimensional manipulation task, which involves a finger learning to spin an anchored object by repeated flicking.

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Section: B Smoothing Methods For Lcpsmentioning

confidence: 99%

Stochastic Complementarity for Local Control of Discontinuous Dynamics

Tassa

Todorov

2010

Robotics: Science and Systems VI

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“…The LCP first emerged as the Karush-Kuhen-Tucker (KKT) optimality conditions for linear programming (LP) and quadratic programming (QP); it has often been described as a fundamental problem Billups and Murty (2000). Besides covering several important classes of mathematical programming problems such as LP, convex quadratic programming (CQP), Nash equilibrium points for nonzero sum games, several economic equilibrium problems and the knapsack problem, the LCP is also used to model many applications such as the contact problem, the obstacle problem, the porous flow problem, the journal bearing problem and many other free boundary problems Wang (2010).…”

Section: Introductionmentioning

confidence: 99%

An active set algorithm for a class of linear complementarity problems arising from rigid body dynamics

Sharaf¹

2016

Pak.j.stat.oper.res.

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An active set algorithm is introduced for positive definite and positive semi definite linear complementarity problems. The proposed algorithm is composed of two phases. Phase 1, the feasibility phase and phase 2, the optimality phase. In phase 1, the ellipsoid method is employed to test for feasibility and provide an advanced starting point if the problem is feasible. Providing such a warm start permits a good estimate of the active set. In phase 2, a criterion based on the complementarity condition is used to detect the working set per iteration until optimality is reached. This criterion leads to a valuable reduction in the size of the problem solved per iteration to obtain a search direction. Numerical examples are solved to illustrate the performance of the algorithm and a practical example in rigid body dynamics is solved to demonstrate the usage of the algorithm to solve such problems.

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“…CC are well known in mathematical programming [1], although not usually in combination with differential equations. In the context of electrical circuits, imposing complementarity conditions simply means that some ports are terminated by ideal diodes, with the current and (minus) the voltage as complementary variables.…”

Section: Introductionmentioning

confidence: 99%

Generalized discontinuous conduction modes in the complementarity formalism

Batlle

Fossas

Merillas³

et al. 2005

IEEE Trans. Circuits Syst. II

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Abstract-We model dc-dc power converters using the complementarity formalism. For each position of the switches, the dynamics is given by a linear complementarity system which incorporates, in a natural way, the description of generalized discontinuous conduction modes (GDCM), characterized by a reduction of the dimension of the effective dynamics. For systems with a single diode, analytical state-space conditions for the presence of a GDCM can be stated. As an example, this result is used to identify the GDCM for the switch configurations of theČuk converter. Simulation results, showing a variety of behaviors, such as persistent or re-entering GDCM, are presented.

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Complementarity problems

Cited by 104 publications

References 4 publications

Stochastic Complementarity for Local Control of Discontinuous Dynamics

Stochastic Complementarity for Local Control of Discontinuous Dynamics

An active set algorithm for a class of linear complementarity problems arising from rigid body dynamics

Generalized discontinuous conduction modes in the complementarity formalism

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