Spielman and Teng finally figured out why the simplex method has worked so well all this time. They did it by developing a new way to analyze the algorithm.

Dongliang Liu, Peng Zheng, Jianghao Wu, Haotian Yin, Linna Zhang, A new method for cylindricity error evaluation based on increment-simplex algorithm, Science ...

Compared with Levenberg Marquardt, the local and initial value sensitive algorithm, Simplex, a global algorithm, is the only robust and easy method which is irrelevant to initial input value.

The original Nelder-Mead simplex algorithm is implemented and extended to boundary constraints. This algorithm does not compute the objective for infeasible points, but it changes the shape of the ...

In this paper, we first propose a perturbation procedure for achieving dual feasibility, which starts with any basis without introducing artificial variables. This procedure and the dual simplex ...

Its services are called upon thousands of times a second to ensure the world's business runs smoothly – but are its mathematics as dependable as we thought?