This paper proposes an explicit solution to the model predictive control of linear systems subject to non-convex polyhedral constraints. These constraints are modeled as the union of a finite number of convex polyhedra. The algorithm is based on calculating the explicit solution to a modified problem with linear constraints defined as the convex hull of the original ones and classifying its reg...

We consider backward stochastic differential equations with convex constraints on the gains (or intensity-of-noise) process. Existence and uniqueness of a minimal solution are established in the case of a drift coefficient which is Lipschitz continuous in the state and gains processes and convex in the gains process. It is also shown that the minimal solution can be characterized as the unique ...

A unified approach is taken for deriving new generalization data dependent bounds for several classes of algorithms explored in the existing literature by different approaches. This unified approach is based on an extension of Vapnik’s inequality for VC classes of sets to random classes of sets that is, classes depending on the random data, invariant under permutation of the data and possessing...

In recent years, the optimization of truss structures has been considered due to their several applications and their simple structure and rapid analysis. DNA computing algorithm is a non-gradient-based method derived from numerical modeling of DNA-based computing performance by new computers with DNA memory known as molecular computers. DNA computing algorithm works based on collective intelli...

We investigate the domain of comprehensive but not necessarily convex bargaining problems. Without convexity the Nash solution is not well de ̄ned. We propose a new solution, the Nash Extension, that coincides with the Nash solution when S is convex. We characterize it by Weak Pareto Optimality, Symmetry, Scale Invariance, Continuity, and a new axiom, Ethical Monotonicity. Journal of Economic Li...

In this articlewe discuss the differential inclusion known as state dependent sweeping process for a class of prox-regular non-convex sets.We associate with any state dependent sweeping process with such sets an unconstraint differential inclusion whose any solution is a solution of the state sweeping process too. We prove a theorem on the existence of a global solution of nonconvex state depen...

In this paper we propose and examine a Vector Supported Convex Hull method for feature subset selection. Within feature subspaces, the method checks locations of vectors belonging to one class with respect to the convex hull of vectors belonging to the other class. Based on such analysis a coefficient is proposed for evaluation of subspace discrimination ability. The method allows for finding s...

In this paper we present that solution of convex programming problems is equivalent with solution of projection formulation, then we introduce neural network models for solving projection formulation and analysis stability conditions and convergence. Simulation shows that the introduced neural network is effective in solving convex programming problems. 2006 Published by Elsevier Inc.

Relative convex hulls have been suggested for multigridconvergent surface area estimation. Besides the existence of a convergence theorem there is no efficient algorithmic solution so far for calculating 3D relative convex hulls. This article discusses an approximative solution based on minimum-length polygon calculations. It is illustrated that this approximative calculation also proves (exper...