Abstract In this paper, we investigate a new primal-dual long-step interior point algorithm for linear optimization. Based on the step size, algorithms can be divided into two main groups, short-step, and methods. practice, variants perform better, but usually, better theoretical complexity achieved short-step One of exceptions is large-update Ai Zhang. The wide neighborhood characteristics pre...

We consider the problem of computing exact sums squares (SOS) decompositions for certain classes non-negative multivariate polynomials, relying on semidefinite programming (SDP) solvers. provide a hybrid numeric-symbolic algorithm rational SOS with coefficients polynomials lying in interior cone. The first step this computes an approximate decomposition perturbation input polynomial arbitrary-p...

Implicit planar curve and surface fitting to a set of scattered points plays an important role in solving a wide variety of problems occurring in computer graphics modelling, computer graphics animation, and computer assisted surgery. The fitted implicit surfaces can be either algebraic or non-algebraic. The main problem with most algebraic surface fitting algorithms is that the surface fitted ...

The rank two Heisenberg–Virasoro algebra can be viewed as a generalization of the twisted algebra. Lie bialgebras play an important role in searching for solutions quantum Yang–Baxter equations. It is interesting to study bialgebra structures on Since brackets are different from that and Virasoro-like algebras, there inner derivations (from itself its tensor space) which hidden more deeply inte...

In this paper, we show that the moving directions of the primal-affine scaling method (with logarithmic barrier function), the dual-affine scaling method (with logarithmic barrier function), and the primal-dual interior point method are merely the Newton directions along three different algebraic "paths" that lead to a solution of the Karush-Kuhn-Tucker conditions of a given linear programming ...

Abstract. The spatial discretization of the unsteady incompressible Navier-Stokes equations is stated as a system of Differential Algebraic Equations (DAEs), corresponding to the conservation of momentum equation plus the constraint due to the incompressibility condition. Runge-Kutta methods applied to the solution of the resulting index-2 DAE system are analyzed, allowing a critical comparison...

In this note we classify all triples (a, b, i) such that there is a convex lattice polygon P with area a, and p respectively i lattice points on the boundary respectively in the interior. The crucial lemma for the classification is the necessity of b ≤ 2 i+7. We sketch three proofs of this fact: the original one by Scott [Sco76], an elementary one, and one using algebraic geometry. As a refinem...

In this note we classify all triples (a, b, i) such that there is a convex lattice polygon P with area a, and b respectively i lattice points on the boundary respectively in the interior. The crucial lemma for the classification is the necessity of b ≤ 2 i+ 7. We sketch three proofs of this fact: the original one by Scott [12], an elementary one, and one using algebraic geometry. As a refinemen...

Sensitivity-based strategies for on-line moving horizon estimation (MHE) and nonlinear model predictive control (NMPC) are presented both from a stability and computational perspective. These strategies make use of full-space interior-point nonlinear programming (NLP) algorithms and NLP sensitivity concepts. In particular, NLP sensitivity allows us to partition the solution of the optimization ...

Theoretical work on two-sided matching markets has focussed on the stable outcomes that are optimal for one side of the market. An innovative exception is a paper by Rochford, who shows how to identify a nonempty set of interior points of the core of the assignment market first studied by Shapley and Shubik. We strengthen Rochfold’s results, by showing that such a set of fixed points must refle...