n-Fold integer programming is a fundamental problem with a variety of natural applications in operations research and statistics. Moreover, it is universal and provides a new, variable-dimension, parametrization of all of integer programming. The fastest algorithm for n-fold integer programming predating the present article runs in time O ( ng(A)L ) with L the binary length of the numerical par...

The simplex method for linear programming can be extended to permit the minimization of any convex separable piecewise-linear objective, subject to linear constraints. Part I of this paper has developed a general and direct simplex algorithm for piecewise-linear programming, under convenient assumptions that guarantee a finite number of basic solutions, existence of basic feasible solutions, an...

1. Abstract An approach to multiobjective optimization is to define a scalar substitute objective function that aggregates all objectives and solve the resulting aggregate optimization problem (AOP). In this paper, we discern that the objective function in quasi-separable multidisciplinary design optimization (MDO) problems can be viewed as such an aggregate objective function (AOF). We consequ...

In this paper, we consider the so-called eventually positive systems, that is systems with trajectories originating in a positive orthant becoming positive after some finite transient. We extend this notion to the input-output system case. Our extension is performed in such a manner, that some valuable properties of internally positive input-output systems are preserved. For example, the stable...

Following the linear programming prescription of Ref. [6], the d ⊗ d Bell diagonal entanglement witnesses are provided. By using Jamiolkowski isomorphism, it is shown that the corresponding positive maps are the generalized qudit Choi maps. Also by manipulating particular d ⊗ d Bell diagonal separable states and constructing corresponding bound entangled states, it is shown that thus obtained d...

Decision circuits perform efficient evaluation of influence diagrams, building on the advances in arithmetic circuits for belief network inference [Darwiche, 2003; Bhattacharjya and Shachter, 2007]. We show how even more compact decision circuits can be constructed for dynamic programming in influence diagrams with separable value functions and conditionally independent subproblems. Once a deci...

In this tutorial, we present optimal Cellular Nonlinear Network (CNN) templates for implementing linearly-separable one-dimensional (1-D) Cellular Automata (CA). From the gallery of CNN templates presented in this paper, one can calculate any of the 256 1-D CA Rules studied by Wolfram using a CNN Universal Machine chip that is several orders of magnitude faster than conventional programming on ...

In this paper we consider a vector integer programming problem with Pareto principle of optimality for the case where partial criteria belong to the class of separable piecewise linear functions. The limit level of the initial data’s perturbations in the space of vector criteria parameters with norms l1 and l∞, preserved Pareto optimality of the solutions is investigated. Formulas of the quasis...