In this short paper we prove that the classic simplex method with the mostnegative-reduced-cost pivoting rule (Dantzig 1947) for solving the Markov decision problem (MDP) with a fixed discount rate is a strongly polynomial-time algorithm. The result seems surprising since this very pivoting rule was shown to be exponential for solving a general linear programming (LP) problem, and the simplex (...

We propose to classify the power of algorithms by the complexity of the problems that they can be used to solve. Instead of restricting to the problem a particular algorithm was designed to solve explicitly, however, we include problems that, with polynomial overhead, can be solved ‘implicitly’ during the algorithm’s execution. For example, we allow to solve a decision problem by suitably trans...

Conventional spherical simplex-radial cubature Kalman filter (SSRCKF) for maneuvering target tracking may decline in accuracy and even diverge when a target makes abrupt state changes. To overcome this problem, a novel algorithm named strong tracking spherical simplex-radial cubature Kalman filter (STSSRCKF) is proposed in this paper. The proposed algorithm uses the spherical simplex-radial (SS...

Ministerial Key Laboratory of JGMT, Nanjing University of Science and Technology, Nanjing 210094, China; [email protected] * Correspondence: [email protected]; Tel.: +86-150-5184-1745 Abstract: For improving the tracking accuracy and model switching speed of maneuvering target tracking in nonlinear systems, a new algorithm named interacting multiple model fifth-degree spherical simplex-radial ...

For improving the tracking accuracy and model switching speed of maneuvering target tracking in nonlinear systems, a new algorithm named the interacting multiple model fifth-degree spherical simplex-radial cubature Kalman filter (IMM5thSSRCKF) is proposed in this paper. The new algorithm is a combination of the interacting multiple model (IMM) filter and the fifth-degree spherical simplex-radia...

We present a simplex algorithm for linear programming in a linear classification formulation. The paramount complexity parameter in linear classification problems is called the margin. We prove that for margin values of practical interest our simplex variant performs a polylogarithmic number of pivot steps in the worst case, and its overall running time is near linear. This is in contrast to ge...

We define the notion of infimum a set points with respect to second order cone. This problem can be showed equivalent minimum ball containing balls and maximum intersecting problem, as well others. present dual algorithm which viewed an extension simplex method solve this problem.

This paper presents a method based on the simplex algorithm to evaluate real or complex polynomials, having scalar or interval coeecients. The aim of this method is not to nd exactly the set P(X) where P is a polynomial and X a real interval or a complex disk but to obtain a set which surely contains P(X). Evaluation de polyn^ omes avec l'agorithme du Simplexe. R esum e : Nous pr esentons ici u...

Pricing is a significant step in the simplex algorithm where an improving nonbasic variable is selected in order to enter the basis. This step is crucial and can dictate the total execution time. In this paper, we perform a computational study in which the pricing operation is computed with eight different pivoting rules: (i) Bland’s Rule, (ii) Dantzig’s Rule, (iii) Greatest Increment Method, (...