A delineability-based method for computing critical sets of algebraic surfaces

A New Method for Determination of Critical Slip Surfaces in Earth Slopes

A New Method for Determination of Critical Slip Surfaces in Earth Slopes

Homotopies for Connected Components of Algebraic Sets with Application to Computing Critical Sets

Given a polynomial system f , this article provides a general construction for homotopies that yield at least one point of each connected component on the set of solutions of f = 0. This algorithmic approach is then used to compute a superset of the isolated points in the image of an algebraic set which arises in many applications, such as computing critical sets used in the decomposition of re...

Computing Roadmaps of General Semi-Algebraic Sets

In this paper we study the problem of determining whether two points lie in the same connected component of a semi-algebraic set S. Although we are mostly concerned with sets S , our algorithm can also decide if points in an arbitrary set S R can be joined by a semi-algebraic path, for any real closed eld R. Our algorithm computes a one-dimensional semi-algebraic subset <(S) of S (actually of a...

A Method for Solving Convex Quadratic Programming Problems Based on Differential-algebraic equations

In this paper, a new model based on differential-algebraic equations(DAEs) for solving convex quadratic programming(CQP) problems is proposed. It is proved that the new approach is guaranteed to generate optimal solutions for this class of optimization problems. This paper also shows that the conventional interior point methods for solving (CQP) problems can be viewed as a special case of the n...