the ellipsoid method is an iterative method for minimizing convex functions over convex sets. The ellipsoid method generates a sequence of ellipsoids whose...

An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation...

the ellipsoid method is exponential in n. But in most applications, R is not so huge. In these cases, the ellipsoid method is the only known method that...

simplex method, which has exponential run-time in the worst case. Practically, they run as fast as the simplex method—in contrast to the ellipsoid method, which...

known for his four-page February 1979 paper that indicated how an ellipsoid method for linear programming can be implemented in polynomial time. The paper...

method. Instead of maintaining the feasible polytope Gt, it maintains an ellipsoid that contains it. Computing the center-of-gravity of an ellipsoid is...

In mathematics, the John ellipsoid or Löwner–John ellipsoid E(K) associated to a convex body K in n-dimensional Euclidean space ⁠ R n {\displaystyle \mathbb...

of the ellipsoid method with the approximate separation oracle is O ( Q m n / δ ) {\displaystyle O(Qmn/\delta )} . During the ellipsoid method, we use...

of a (which is not quite 6,400 km). Many methods exist for determination of the axes of an Earth ellipsoid, ranging from meridian arcs up to modern satellite...

efficient algorithm that solves these problems in polynomial time. The ellipsoid method is also polynomial time but proved to be inefficient in practice. Denoting...

minimization problems (similar to conjugate gradient methods). Ellipsoid method: An iterative method for small problems with quasiconvex objective functions...

nonlinear programming. It can still be solved in polynomial time by the ellipsoid method if the objective function is convex; otherwise the problem may be NP...

optimization and is best known for his work on the ellipsoid method, modern interior-point methods and robust optimization. Nemirovski earned a Ph.D....

In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding...

method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of an iterative method or a method of...

the introduction of the ellipsoid method. The convergence analysis has (real-number) predecessors, notably the iterative methods developed by Naum Z. Shor...

the simplex algorithm, or in worst-case polynomial time using the ellipsoid method, each specialization has a smaller solution space and thus more efficient...

the angle formed between the vector perpendicular (or normal) to the ellipsoidal surface from the point, and the plane of the equator. Two levels of abstraction...

dimensions of the Earth ellipsoid axes were defined by logarithms in keeping with former calculation methods. The Bessel ellipsoid fits especially well to...

nearest integer. The solution method for semidefinite programs, used by this algorithm, is based on the ellipsoid method for linear programming. It leads...

Khachiyan, Martin Grötschel, László Lovász and Alexander Schrijver for the ellipsoid method in linear programming and combinatorial optimization. G. P. Egorychev...

The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth...

a method to describe a convex set that is given as an input to an optimization algorithm. Separation oracles are used as input to ellipsoid methods.: 87...

Lagrangian methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods in that they...

Lecture 17" (PDF). Grötschel, M.; Lovasz, L.; Schrijver, A. (1981). "The ellipsoid method and its consequences in combinatorial optimization". Combinatorica...

standards, also includes a choice of geodetic datum (including an Earth ellipsoid), as different datums will yield different latitude and longitude values...

astro-geodetic methods already described.) The sole contribution of satellite data to the development of WGS 60 was a value for the ellipsoid flattening which...

Wolfe, etc.). For positive definite Q, when the problem is convex, the ellipsoid method solves the problem in (weakly) polynomial time. Ye and Tse present...

polynomial-time approximation scheme for the Lovász number, based on the ellipsoid method and provided by Grötschel, Lovász & Schrijver (1981). Approximating...

In numerical analysis, a quasi-Newton method is an iterative numerical method used either to find zeroes or to find local maxima and minima of functions...