The purpose of this post is to detail work done by Dan Melanz and I on the topic of solving frictional contact problems using the General Algebraic Modeling System (GAMS)

The best way to describe GAMS is that it is a language and framework for writing mathematical programming and optimization problems. GAMS can solve many different classes of problems, in this post the Nonlinear Programming (NLP), Quadratically Constrained Program (QCP) and Extended Mathematical Program (EMP) problem types will be discussed.

## References

These papers provide more details about the various formulations used in this post.

#### Primal Model:

V. Acary and F. Cadoux, “Applications of an Existence Result for the Coulomb Friction Problem,” Recent Advances in Contact Mechanics, pp. 45–66, 2013.

V. Acary, F. Cadoux, C. Lemaréchal, and J. Malick, “A formulation of the linear discrete Coulomb friction problem via convex optimization,” Z. angew. Math. Mech., vol. 91, no. 2, pp. 155–175, Feb. 2011.

F. Bertails-Descoubes, F. Cadoux, G. Daviet, and V. Acary, “A nonsmooth Newton solver for capturing exact Coulomb friction in fiber assemblies,” ACM Transactions on Graphics, vol. 30, no. 1, pp. 1–14, Jan. 2011.

#### Dual Model:

M. Anitescu and G. D. Hart, “A constraint-stabilized time-stepping approach for rigid multibody dynamics with joints, contact and friction,” Int. J. Numer. Meth. Engng., vol. 60, no. 14, pp. 2335–2371, Aug. 2004.

A. Tasora and M. Anitescu, “A complementarity-based rolling friction model for rigid contacts,” Meccanica, vol. 48, no. 7, pp. 1643–1659, Sep. 2013.