We consider the following problem: Given a rational matrix A ∈ Qm×n and a rational polyhedron Q ⊆ Rm+p, decide if for all vectors b ∈ Rm, for which there exists an integral z ∈ Zp such that (b,z) ∈ Q, the system of linear inequalities Ax 6 b has an integral solution. We show that there exists an algorithm that solves this problem in polynomial time if p and n are fixed. This extends a result of...

We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based on recently developed parametric programming algorithms. We first describe how we can recast and solve the inner (follower’s) problem of the bilevel formulation as a multi-parametric programming problem, with parameters being the (unknown) variables of the outer (leader’s) ...

General idea of nonlinear correcting factors that was successfully applied to accelerate and derive algorithms for many linear and nonlinear problems is used to develop several efficient procedures for solving linear systems of equations based on the Jacobi algorithm. Results of the theoretical study and extensive computer experiments for stochastic matrices are presented and analyzed to determ...

The paper deals with a short presentation of the basic ideas concerning the multiparametric quadratic programming (mp-QP) problems. The model predictive control is considered also as particular mp-QP problem. Since the solutions to mp-QP problems can be expressed as piecewise affine linear functions of the state, a new implementation in terms of adaptive network-based fuzzy inference systems is...

This paper describes an approach based on formal calculus to optimize trajectories described by a succession of discrete states, by means of combining the Dynamic Programming technique with the formal approach presented in [Cardillo et 2001]. This approach allows to obtain an explicit form of the optimal control sequence, based on formal calculus. It also allows to introduce parameters in the s...

Recently, a comprehensive dynamic mathematical model named Copernicus has been established to discover the mechanism of the vascular bubble formation and growth during and after decompression from a dive. The model uses Venous Gas Emboli (VGE) as a measurement and connects it to the risk of severe Decompression Sickness (DCS). Being validated by a series of diving tests, Copernicus model is bel...

Narasimhan incorporated fuzzy set theory within goal formulation in 1980. Since then, much research has been performed in this field, and various models for solving fuzzy goal programming have been proposed. One of the well-known models was proposed by Tiwari et al. in 1987 [19], where an additive model was proposed. This paper is an extension to the Tiwari et al. model that deals with the sum ...

In this paper, a fast bounded parametric margin  -support vector machine (BP- SVM) for classification is proposed. Different from the parametric margin  -support vector machine (par- -SVM), the BP- -SVM maximizes a bounded parametric margin, and consequently the successive overrelaxation (SOR) technique could be used to solve our dual problem as opposed solving the standard quadratic progr...