Maximum 200 words) As an emerging effective approach to nonlinear robust control, simplex sliding mode control demonstrates some attractive features not possessed by the conventional sliding mode control method, from both theoretical and practical points of view. However, no systematic approach is currently available for computing the simplex control vectors in nonlinear sliding mode control. I...

When solving families of related linear programming (LP) problems and many classes of single LP problems, the simplex method is the preferred computational technique. Hitherto there has been no efficient parallel implementation of the simplex method that gives good speed-up on general, large sparse LP problems. This paper presents a variant of the dual simplex method and a prototype parallelisa...

We propose quantum subroutines for the simplex method that avoid classical computation of basis inverse. For an \(m \times n\) constraint matrix with at most \(d_c\) nonzero elements per column, d column or row basis, condition number \(\kappa \), and optimality tolerance \(\epsilon we show pricing can be performed in \(\tilde{O}(\frac{1}{\epsilon }\kappa \sqrt{n}(d_c n + m))\) time, where \(\t...